id stringlengths 39 39 | setting_key stringclasses 1
value | setting_name stringclasses 0
values | messages listlengths 1 1 | ground_truth stringclasses 70
values | dataset stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_derivative_sign_train_0100 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(1(-1((1x - 1)/(2x - 3)) + 3)^2 - 2(-1((1x - 1)/(2x - 3)) + 3) + 4) - 2| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0101 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(2((-3x + 2)/(2x - 1))^2 - 3((-3x + 2)/(2x - 1)) - 4) + 3| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0102 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((1(1|(2x + 3) - 1| + 1) + 1)/(2(1|(2x + 3) - 1| + 1) - 3))^2 - 3((1(1|(2x + 3) - 1| + 1) + 1)/(2(1|(2x + 3) - 1| + 1) - 3)) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your ... | 2 | math |
algebra_func_derivative_sign_train_0103 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(1|(5(-2cos(1πx + 1) + 3)^2 + 4(-2cos(1πx + 1) + 3) - 3) + 1| + 3) + 2)/(-2(1|(5(-2cos(1πx + 1) + 3)^2 + 4(-2cos(1πx + 1) + 3) - 3) + 1| + 3) - 3) positive?\n\nPresent the answer in LaTex for... | 10 | math |
algebra_func_derivative_sign_train_0104 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(3x^2 - 5x - 5) - 1| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0105 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-1(-4(1|x|)^2 + 1(1|x|) + 4) - 4) + 2)/(-3(-1(-4(1|x|)^2 + 1(1|x|) + 4) - 4) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0106 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1e^(-1(-4x^2 - 2x - 5)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0107 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-1|x + 2| - 1)^2 + 4(-1|x + 2| - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0108 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(3|((1(2x + 1) - 3)/(-1(2x + 1) + 2)) + 2| + 3)^2 + 1(3|((1(2x + 1) - 3)/(-1(2x + 1) + 2)) + 2| + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0109 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1sin(3π(-1x^2 - 2x + 2) + 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 49 | math |
algebra_func_derivative_sign_train_0110 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 3|((3(-1cos(1πx - 1) - 2) + 3)/(-1(-1cos(1πx - 1) - 2) - 2))| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 21 | math |
algebra_func_derivative_sign_train_0111 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1sin(1π((-1(1x + 1) - 3)/(2(1x + 1) + 1)) + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
algebra_func_derivative_sign_train_0112 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(2|(5(3cos(1πx - 2) - 2)^2 + 3(3cos(1πx - 2) - 2) + 3) + 3| + 3))/(-3(2|(5(3cos(1πx - 2) - 2)^2 + 3(3cos(1πx - 2) - 2) + 3) + 3| + 3) - 2) is strictly decreasing.\n\nPresent the answer... | 21 | math |
algebra_func_derivative_sign_train_0113 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(1π(1x - 3) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 10 | math |
algebra_func_derivative_sign_train_0114 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1|(-1cos(2π((-1x)/(2x - 1)) - 3) + 2)| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0115 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(-3|(-1(1cos(2πx - 2) + 3)^2 + 4)| - 1))/(-3(-3|(-1(1cos(2πx - 2) + 3)^2 + 4)| - 1) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 20 | math |
algebra_func_derivative_sign_train_0116 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-3(1cos(2π((-3x)/(-3x + 1)) - 3) + 1)^2 + 2(1cos(2π((-3x)/(-3x + 1)) - 3) + 1) + 4) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
algebra_func_derivative_sign_train_0117 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((1(3cos(1π(2x^2 - 3x + 3) - 3) - 1) + 3)/(3(3cos(1π(2x^2 - 3x + 3) - 3) - 1) - 1)) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 53 | math |
algebra_func_derivative_sign_train_0118 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-4((-1x - 1)/(3x + 1))^2 - 3((-1x - 1)/(3x + 1)))| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0119 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(3π((-3(4(5x^2 + 2x - 2) - 5) - 3)/(1(4(5x^2 + 2x - 2) - 5))) + 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 4 | math |
algebra_func_derivative_sign_train_0120 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 3|(-5x^2 - 4x + 5)| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0121 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -4((2(-2sin(2πx) - 2) + 3)/(-2(-2sin(2πx) - 2) + 3)) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 20 | math |
algebra_func_derivative_sign_train_0122 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(3π(2x^2 - 2) - 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 43 | math |
algebra_func_derivative_sign_train_0123 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(4((1x + 2)/(-3x - 2)) - 1)| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0124 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(3π(-5x + 3) + 1) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 52 | math |
algebra_func_derivative_sign_train_0125 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(3sin(1πx) - 2) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 10 | math |
algebra_func_derivative_sign_train_0126 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1e^(2(-5(4x^2 - 4x - 2) - 5)) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0127 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(3π((1x - 2)/(-2x + 1)) - 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 7 | math |
algebra_func_derivative_sign_train_0128 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1sin(3π(3((-1(-1x^2 + 1x + 2) + 3)/(3(-1x^2 + 1x + 2) - 2)) - 5) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 13 | math |
algebra_func_derivative_sign_train_0129 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(1π(2|x + 3| - 3) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 20 | math |
algebra_func_derivative_sign_train_0130 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4((-3x + 1)/(-1x))^2 + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0131 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1|(3sin(3πx - 1) - 3) - 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 30 | math |
algebra_func_derivative_sign_train_0132 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(3|(-3x + 3)| - 1)^2 + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0133 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -2(-2(1cos(1π(2|x - 1| + 3) + 3) + 1) + 5)^2 + 3(-2(1cos(1π(2|x - 1| + 3) + 3) + 1) + 5) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 20 | math |
algebra_func_derivative_sign_train_0134 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((-2(2|x - 3|) - 1)/(1(2|x - 3|) - 3))^2 - 3((-2(2|x - 3|) - 1)/(1(2|x - 3|) - 3)) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0135 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 2((-3(-3cos(3πx - 3)) - 1)/(-1(-3cos(3πx - 3)) + 2)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 30 | math |
algebra_func_derivative_sign_train_0136 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5((-3(4x + 4) - 1)/(3(4x + 4) + 3))^2 - 1((-3(4x + 4) - 1)/(3(4x + 4) + 3)) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0137 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-1(2cos(1πx) - 1) - 1)^2 + 2(-1(2cos(1πx) - 1) - 1) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 20 | math |
algebra_func_derivative_sign_train_0138 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-4(-3cos(3πx + 3) + 2)^2 - 2(-3cos(3πx + 3) + 2) + 2)| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 38 | math |
algebra_func_derivative_sign_train_0139 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-5(-2|x| + 1) + 3)^2 - 4(-5(-2|x| + 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0140 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((-2(-3x - 5) - 3)/(-3(-3x - 5) + 1))^2 - 2((-2(-3x - 5) - 3)/(-3(-3x - 5) + 1)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0141 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((-1(5(-1x^2 + 4x - 3) - 4) - 1)/(-2(5(-1x^2 + 4x - 3) - 4) + 1)) - 2| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0142 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-2|(1x - 4) - 2| + 1)^2 + 1(-2|(1x - 4) - 2| + 1) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0143 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -3|(-2(1x + 3)^2 + 2) + 1| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0144 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-5(-2(-2|x + 2| + 3))^2 - 5(-2(-2|x + 2| + 3))) - 1)/(1(-5(-2(-2|x + 2| + 3))^2 - 5(-2(-2|x + 2| + 3))) + 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0145 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = (1(2(-1sin(3π(5x^2 + 5x - 2) + 1) - 3) - 3) + 3)/(-3(2(-1sin(3π(5x^2 + 5x - 2) + 1) - 3) - 3)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 49 | math |
algebra_func_derivative_sign_train_0146 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -4(-2|(2x + 3) + 3| + 1)^2 + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0147 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((-3(-4(-1x - 4)^2 + 1(-1x - 4) - 4))/(2(-4(-1x - 4)^2 + 1(-1x - 4) - 4) + 2)) + 2| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0148 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-2|(-3((-1x + 3)/(-1x + 2)) + 2) - 1| + 2)^2 + 5(-2|(-3((-1x + 3)/(-1x + 2)) + 2) - 1| + 2) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0149 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(3π(2x + 4) - 2) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 61 | math |
algebra_func_derivative_sign_train_0150 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1|(-1cos(3πx - 1) + 1) - 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 61 | math |
algebra_func_derivative_sign_train_0151 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1cos(3π(-1x - 3) - 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 31 | math |
algebra_func_derivative_sign_train_0152 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 2((-3(1cos(1πx + 1) + 1) - 3)/(2(1cos(1πx + 1) + 1) + 1))^2 - 3((-3(1cos(1πx + 1) + 1) - 3)/(2(1cos(1πx + 1) + 1) + 1)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your ... | 10 | math |
algebra_func_derivative_sign_train_0153 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(1π(5x + 2) + 3) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 50 | math |
algebra_func_derivative_sign_train_0154 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(3|(-2x^2 - 2x + 1) - 1| - 2) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0155 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(3(-2|x - 1|)^2 + 1(-2|x - 1|) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0156 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1sin(3πx) + 1) + 1)/(-1(1sin(3πx) + 1) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 31 | math |
algebra_func_derivative_sign_train_0157 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(1e^(1(4x^2 - 5x - 5))))/(-1(1e^(1(4x^2 - 5x - 5))) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0158 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1sin(2π(1(1(-3|x + 2|) + 5)^2 + 3(1(-3|x + 2|) + 5) - 4) - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 54 | math |
algebra_func_derivative_sign_train_0159 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1sin(1π(-5((3x)/(1x + 1)) + 4) - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 17 | math |
algebra_func_derivative_sign_train_0160 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-3|((-1(-5x^2 + 2x + 1) - 3)/(-1(-5x^2 + 2x + 1) + 2)) + 2|) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0161 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1(-2|(4((-2x - 2)/(-2x))^2 + 5((-2x - 2)/(-2x)) - 4) + 2| - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0162 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|((2(1x + 4))/(-2(1x + 4) + 3)) - 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0163 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(2π(4(-4((3x - 2)/(2x + 2))^2 - 5) - 2) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 43 | math |
algebra_func_derivative_sign_train_0164 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(1|x - 3|)^2 - 3(1|x - 3|) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0165 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1sin(3π(2|x + 3| + 2) + 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 60 | math |
algebra_func_derivative_sign_train_0166 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 3((-1(1|x - 1| - 3) + 3)/(-2(1|x - 1| - 3) - 2))^2 - 4((-1(1|x - 1| - 3) + 3)/(-2(1|x - 1| - 3) - 2)) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0167 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(3cos(3πx + 2) + 1)^2 - 3(3cos(3πx + 2) + 1) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 61 | math |
algebra_func_derivative_sign_train_0168 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1|(2sin(1π((2x + 1)/(2x + 2)) + 1) - 1) + 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
algebra_func_derivative_sign_train_0169 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(3π(3|x + 2| - 2) + 3) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 91 | math |
algebra_func_derivative_sign_train_0170 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-3cos(2π(-1|x + 3| - 2) - 2) - 1) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 21 | math |
algebra_func_derivative_sign_train_0171 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(-2sin(1πx - 1) - 3)^2 + 3(-2sin(1πx - 1) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 10 | math |
algebra_func_derivative_sign_train_0172 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1((-2(1|x + 1| - 1))/(3(1|x + 1| - 1) - 2))^2 - 2((-2(1|x + 1| - 1))/(3(1|x + 1| - 1) - 2)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0173 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((3(1(3|x - 2| - 2)) + 2)/(-1(1(3|x - 2| - 2))))^2 + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0174 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 3|(3sin(3πx)) + 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 31 | math |
algebra_func_derivative_sign_train_0175 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(2π((1(-2x^2 + 1x + 4) + 3)/(3(-2x^2 + 1x + 4) + 2)) + 2) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 6 | math |
algebra_func_derivative_sign_train_0176 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = (-1(-2cos(3π(2x + 3) + 2) - 1))/(-1(-2cos(3π(2x + 3) + 2) - 1) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 61 | math |
algebra_func_derivative_sign_train_0177 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(3(-2e^(-1(3|x + 2|)) + 1)^2 - 4(-2e^(-1(3|x + 2|)) + 1) - 4) - 1)/(-1(3(-2e^(-1(3|x + 2|)) + 1)^2 - 4(-2e^(-1(3|x + 2|)) + 1) - 4) - 2) is strictly decreasing.\n\nPresent the answer in... | 2 | math |
algebra_func_derivative_sign_train_0178 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(1sin(2π(-3|x - 1|) + 3) + 2)^2 - 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 61 | math |
algebra_func_derivative_sign_train_0179 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((3(1e^(-1(3x + 2)) - 2))/(-1(1e^(-1(3x + 2)) - 2) + 2))^2 + 4((3(1e^(-1(3x + 2)) - 2))/(-1(1e^(-1(3x + 2)) - 2) + 2)) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer... | 2 | math |
algebra_func_derivative_sign_train_0180 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -5((-2x)/(-3x - 1))^2 + 2((-2x)/(-3x - 1)) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0181 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(2π(-1(2x + 3)^2 + 3(2x + 3)) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 56 | math |
algebra_func_derivative_sign_train_0182 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -2(-1cos(1π(-1((2x + 2)/(-3x)) - 5) + 2) - 3)^2 - 3(-1cos(1π(-1((2x + 2)/(-3x)) - 5) + 2) - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 3 | math |
algebra_func_derivative_sign_train_0183 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-1sin(1πx + 2) - 2)^2 + 2(-1sin(1πx + 2) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
algebra_func_derivative_sign_train_0184 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 4(-3|x + 1| + 2)^2 + 2(-3|x + 1| + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0185 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(3π(1x^2 + 2x) + 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 49 | math |
algebra_func_derivative_sign_train_0186 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = (3(3cos(1π(4x + 4) + 3) - 1) - 3)/(-1(3cos(1π(4x + 4) + 3) - 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 41 | math |
algebra_func_derivative_sign_train_0187 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-1sin(1π(3(3|x - 3| + 3) - 2) + 1) - 1)^2 - 1(-1sin(1π(3(3|x - 3| + 3) - 2) + 1) - 1) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 81 | math |
algebra_func_derivative_sign_train_0188 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(3(2|(-2x^2 + 3x + 3) + 2|) + 4) - 3)/(-3(3(2|(-2x^2 + 3x + 3) + 2|) + 4) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0189 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -2sin(2π(-2x^2 - 1x - 3)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 47 | math |
algebra_func_derivative_sign_train_0190 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(3e^(1(2|x + 3| - 2)) - 2)^2 - 3(3e^(1(2|x + 3| - 2)) - 2) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0191 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-1|(-2cos(1π(1x - 3) - 1) + 1)| + 1)^2 + 4(-1|(-2cos(1π(1x - 3) - 1) + 1)| + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 21 | math |
algebra_func_derivative_sign_train_0192 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(2(3|(-2x^2 - 3x - 3) + 2| - 2) - 5) - 1)/(-1(2(3|(-2x^2 - 3x - 3) + 2| - 2) - 5)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0193 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1|x - 1| + 3)^2 - 4(-1|x - 1| + 3) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0194 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-3(-2sin(3π(5x^2 - 5x - 4) - 1) - 1))| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 8 | math |
algebra_func_derivative_sign_train_0195 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -2((-1(3cos(1πx - 2) + 2) + 1)/(-1(3cos(1πx - 2) + 2) - 2))^2 - 1((-1(3cos(1πx - 2) + 2) + 1)/(-1(3cos(1πx - 2) + 2) - 2)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Yo... | 21 | math |
algebra_func_derivative_sign_train_0196 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1e^(1(-3(1|((2x - 1)/(2x + 2)) - 3| - 3)^2 - 3(1|((2x - 1)/(2x + 2)) - 3| - 3) + 4)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0197 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(2π((2x + 2)/(-2x)) + 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 5 | math |
algebra_func_derivative_sign_train_0198 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = 1(-3|x - 1| - 2)^2 + 5(-3|x - 1| - 2) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 2 | math |
algebra_func_derivative_sign_train_0199 | algebra_func_derivative_sign | null | [
{
"role": "user",
"content": "For the function f(x) = -1((-3(-1sin(1π(1|x + 2| - 2) - 3) - 2) + 2)/(1(-1sin(1π(1|x + 2| - 2) - 3) - 2))) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] | 11 | math |
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