id
stringlengths 29
29
| setting_key
stringclasses 1
value | setting_name
stringclasses 0
values | messages
listlengths 1
1
| ground_truth
stringclasses 186
values | dataset
stringclasses 1
value |
|---|---|---|---|---|---|
algebra_func_zeros_train_0100
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 4(5(-2|((2x - 2)/(3x + 3))| + 2)^2 + 3(-2|((2x - 2)/(3x + 3))| + 2)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0101
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(1|x + 3| - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0102
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3cos(1π(2(1|(-5x - 3) + 2| + 2)^2 - 4(1|(-5x - 3) + 2| + 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1580
|
math
|
algebra_func_zeros_train_0103
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(1|((1x - 2)/(-3x)) - 3| + 1)^2 - 4(1|((1x - 2)/(-3x)) - 3| + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0104
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3((3(1(-2|x| - 1)^2 + 2(-2|x| - 1) + 1) + 1)/(2(1(-2|x| - 1)^2 + 2(-2|x| - 1) + 1) + 2)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0105
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3e^(-1((-3(2x^2 - 3x - 1) + 2)/(2(2x^2 - 3x - 1) + 3))) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0106
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3(-2x + 5)^2 + 4(-2x + 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0107
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-2(1(-1(-3|x - 1| - 2)^2 - 1(-3|x - 1| - 2) + 3) + 2))/(-3(1(-1(-3|x - 1| - 2)^2 - 1(-3|x - 1| - 2) + 3) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0108
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2((-1(-2e^(1(-3x - 4)) + 1) - 3)/(1(-2e^(1(-3x - 4)) + 1) + 1))^2 - 5((-1(-2e^(1(-3x - 4)) + 1) - 3)/(1(-2e^(1(-3x - 4)) + 1) + 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0109
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1|(4x - 1) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0110
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3(-2|x + 3| + 1)^2 - 1(-2|x + 3| + 1) + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0111
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1((3(-2(-3|x| + 3)^2 + 5(-3|x| + 3) + 5) - 1)/(1(-2(-3|x| + 3)^2 + 5(-3|x| + 3) + 5))) - 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0112
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3|(5(-2x^2 - 1x + 4) - 4) + 1| - 1) + 2)/(1(3|(5(-2x^2 - 1x + 4) - 4) + 1| - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0113
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -3|(-3cos(3πx + 3) - 2) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0114
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1((-2x - 1)/(-3x + 2))^2 + 2((-2x - 1)/(-3x + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0115
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1((2(-3cos(2πx - 3) + 1) - 2)/(2(-3cos(2πx - 3) + 1) - 1)) + 1)^2 + 1(1((2(-3cos(2πx - 3) + 1) - 2)/(2(-3cos(2πx - 3) + 1) - 1)) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
80
|
math
|
algebra_func_zeros_train_0116
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(-1x^2 + 4x + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0117
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|((3x - 1)/(-3x + 4)) + 2| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0118
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (1(-3|x - 3|) + 2)/(-2(-3|x - 3|) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0119
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3(-3x)^2 + 2(-3x) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0120
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2π((1(1x + 3) - 1)/(-1(1x + 3) + 2))) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
42
|
math
|
algebra_func_zeros_train_0121
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5(5x^2 + 1x - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0122
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 5(3cos(2πx - 3) - 3)^2 + 5(3cos(2πx - 3) - 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0123
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(2(-2|x + 2| + 2) + 2) - 1)/(-1(2(-2|x + 2| + 2) + 2)))^2 - 1((-3(2(-2|x + 2| + 2) + 2) - 1)/(-1(2(-2|x + 2| + 2) + 2))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0124
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1cos(1π(1|x + 3|) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0125
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-1(3|(1(3x - 5)^2 + 5(3x - 5) + 1) + 1|) + 2)/(-2(3|(1(3x - 5)^2 + 5(3x - 5) + 1) + 1|) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0126
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((1(2x^2 + 1x + 3) - 3)/(2(2x^2 + 1x + 3) + 2)) - 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0127
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1π(2|x| - 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0128
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 3((-3x - 1)/(2x - 3))^2 - 1((-3x - 1)/(2x - 3)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0129
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (1(2(3x^2 + 1x - 4) + 5) + 3)/(1(2(3x^2 + 1x - 4) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0130
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2(5(-2sin(1πx - 3))^2 + 1(-2sin(1πx - 3)) + 1) + 3)/(-3(5(-2sin(1πx - 3))^2 + 1(-2sin(1πx - 3)) + 1) - 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0131
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2|(1e^(-1(-1((1x + 2)/(-1x + 3)) + 4)) - 2) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0132
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (-1(-2|(2e^(2(-3x^2 - 5x + 4))) - 3| - 1) - 2)/(-3(-2|(2e^(2(-3x^2 - 5x + 4))) - 3| - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0133
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -2((1(1x + 4) - 3)/(2(1x + 4) - 1))^2 + 2((1(1x + 4) - 3)/(2(1x + 4) - 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0134
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2e^(-2x) + 2)^2 + 5(-2e^(-2x) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0135
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3e^(2(-4((2x - 1)/(2x + 3))^2 + 5((2x - 1)/(2x + 3)) + 5)) + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0136
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1((-3(1(2|x - 1| - 1)) - 1)/(-1(1(2|x - 1| - 1)) - 1))^2 + 5((-3(1(2|x - 1| - 1)) - 1)/(-1(1(2|x - 1| - 1)) - 1)) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0137
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2|(3(-2x - 4)^2 + 5(-2x - 4) - 1)| + 1))/(1(-2|(3(-2x - 4)^2 + 5(-2x - 4) - 1)| + 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0138
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1sin(1π(-2|x - 2| - 2) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0139
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3((-1(2|(-2x + 3) - 3| + 1) + 3)/(-3(2|(-2x + 3) - 3| + 1) + 4))^2 + 2((-1(2|(-2x + 3) - 3| + 1) + 3)/(-3(2|(-2x + 3) - 3| + 1) + 4)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0140
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -1(-2(-1|((3x - 3)/(1x - 2)) - 3| + 1)^2 - 4(-1|((3x - 3)/(1x - 2)) - 3| + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0141
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3sin(2π(2|x - 2| + 2)) - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
57
|
math
|
algebra_func_zeros_train_0142
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3|(1((-3(-5x - 1) - 2)/(2(-5x - 1) + 1))^2 - 1((-3(-5x - 1) - 2)/(2(-5x - 1) + 1))) - 3| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0143
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -3sin(2π(2|(5x^2 - 2x + 4) - 2| - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1723
|
math
|
algebra_func_zeros_train_0144
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -2|(3x - 4)| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0145
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1|(1(1((-2x + 3)/(-2x - 1))^2 - 1((-2x + 3)/(-2x - 1)) - 1) - 1) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0146
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3π(-1|x - 2| - 2) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
60
|
math
|
algebra_func_zeros_train_0147
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (1(3(-4(-1|x + 3| + 1)^2 + 5) + 4) - 3)/(2(3(-4(-1|x + 3| + 1)^2 + 5) + 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0148
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(3x^2 - 1) + 5) + 2)/(-3(-1(3x^2 - 1) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0149
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(-3sin(2πx + 1) - 2)^2 - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0150
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 1(-1((-3x + 1)/(3x - 2)) + 1)^2 - 2(-1((-3x + 1)/(3x - 2)) + 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0151
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3cos(2π(-2|((2(3x) + 3)/(2(3x) - 3)) + 1| - 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
71
|
math
|
algebra_func_zeros_train_0152
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 5(4x + 1)^2 - 4(4x + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0153
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3sin(3π(1x^2 + 3x - 1) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
278
|
math
|
algebra_func_zeros_train_0154
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1((3x - 2)/(1x - 3))^2 + 4((3x - 2)/(1x - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0155
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (-3(-2|(2cos(3π(-4x) + 1) - 3) + 2| + 3) + 3)/(3(-2|(2cos(3π(-4x) + 1) - 3) + 2| + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
360
|
math
|
algebra_func_zeros_train_0156
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) - 3) + 2)/(-3(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0157
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-2(3sin(1π(2|(-1x - 1) - 3|)) + 3))/(2(3sin(1π(2|(-1x - 1) - 3|)) + 3) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0158
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(1|((2x + 1)/(2x + 2)) - 3| - 3)^2 - 3(1|((2x + 1)/(2x + 2)) - 3| - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
3
|
math
|
algebra_func_zeros_train_0159
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1(1((-3x - 3)/(-1x - 2)) + 2)^2 - 4(1((-3x - 3)/(-1x - 2)) + 2) + 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0160
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3(-1(-1|(-3sin(3πx - 1)) + 1| - 1)^2 + 3(-1|(-3sin(3πx - 1)) + 1| - 1) + 3) - 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
110
|
math
|
algebra_func_zeros_train_0161
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 4(2x + 2)^2 + 2(2x + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0162
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2π(2|((1x)/(-1x - 2)) - 3| + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
103
|
math
|
algebra_func_zeros_train_0163
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 3((-3(1(-2|x + 1| - 3) + 5) - 1)/(1(1(-2|x + 1| - 3) + 5) - 3))^2 + 4((-3(1(-2|x + 1| - 3) + 5) - 1)/(1(1(-2|x + 1| - 3) + 5) - 3)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0164
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3π(-2(1|(3x - 4) + 1| - 2)^2 - 3(1|(3x - 4) + 1| - 2) - 1) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1471
|
math
|
algebra_func_zeros_train_0165
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -3((-3(3(-2|x|)^2 - 2(-2|x|) - 1) - 1)/(2(3(-2|x|)^2 - 2(-2|x|) - 1))) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0166
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -5(-3x^2 + 1x + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0167
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3(1(3e^(-1(3|x - 2| - 3)) - 1)^2 + 5(3e^(-1(3|x - 2| - 3)) - 1) - 1) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0168
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(-2sin(2πx + 2))^2 + 5(-2sin(2πx + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0169
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 1(2e^(2((2x + 1)/(-1x + 2))) - 2)^2 - 4(2e^(2((2x + 1)/(-1x + 2))) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0170
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -4(2|x + 3|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0171
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1(2|(3cos(3π(-1x^2 - 4x + 4) - 2) - 1) - 2| - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
579
|
math
|
algebra_func_zeros_train_0172
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -2sin(3π(-4(4((-3x - 1)/(-2x - 2))^2 + 4((-3x - 1)/(-2x - 2)) + 1) - 4) - 2) + 1 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
427
|
math
|
algebra_func_zeros_train_0173
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation -5(1|((3x + 2)/(-1x - 2)) + 1|) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0174
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-3(3sin(3πx - 1) + 2) + 2)/(2(3sin(3πx - 1) + 2) - 1)) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0175
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1|((-1(3sin(3πx) + 1) - 2)/(-2(3sin(3πx) + 1) - 3)) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
120
|
math
|
algebra_func_zeros_train_0176
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 3cos(2π(-4((-3(2x - 3) - 3)/(1(2x - 3) + 2))^2 - 2((-3(2x - 3) - 3)/(1(2x - 3) + 2)) - 5) + 3) + 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
214
|
math
|
algebra_func_zeros_train_0177
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 5((-2(-2|x + 2|) - 1)/(-1(-2|x + 2|) - 1)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0178
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3|(-1((1x)/(-1x + 2))^2 - 4((1x)/(-1x + 2)) - 1) + 1| + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0179
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 5((-1(2|(-3cos(2πx + 2) + 1) + 2| - 3) + 3)/(-3(2|(-3cos(2πx + 2) + 1) + 2| - 3) - 1))^2 - 3((-1(2|(-3cos(2πx + 2) + 1) + 2| - 3) + 3)/(-3(2|(-3cos(2πx + 2) + 1) + 2| - 3) - 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
80
|
math
|
algebra_func_zeros_train_0180
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1cos(3π(3|((-2x)/(-2x + 3)) + 1| + 2) + 1) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
126
|
math
|
algebra_func_zeros_train_0181
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1π(-2((2x - 1)/(3x - 1))^2 + 4((2x - 1)/(3x - 1)) - 1) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
14
|
math
|
algebra_func_zeros_train_0182
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = (3(3cos(1π(-5x^2 + 5x + 5) + 2) + 1) + 2)/(-1(3cos(1π(-5x^2 + 5x + 5) + 2) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
906
|
math
|
algebra_func_zeros_train_0183
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-5((2(-1|x| + 2) - 3)/(1(-1|x| + 2) + 2)))^2 + 1(-5((2(-1|x| + 2) - 3)/(1(-1|x| + 2) + 2))) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0184
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 2(1x^2 - 2x - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0185
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1((1(-4(-2cos(2πx - 3) + 1) - 1))/(-3(-4(-2cos(2πx - 3) + 1) - 1) + 4))^2 + 4 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
80
|
math
|
algebra_func_zeros_train_0186
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2cos(1π(-4x - 5) - 1) - 2 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
40
|
math
|
algebra_func_zeros_train_0187
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = 2|(-4(2x + 5)^2 - 5(2x + 5) - 2) + 1| - 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0188
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (1(2x^2 - 5) - 2)/(-2(2x^2 - 5) - 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0189
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-3(-2|(4x - 4) - 1| + 1) - 3)/(1(-2|(4x - 4) - 1| + 1) - 2) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0190
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(-2(3((-1x + 1)/(2x + 2))^2 - 4((-1x + 1)/(2x + 2)) - 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0191
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation (2(-3|(-1x^2 - 2x + 5) + 2|) + 1)/(-3(-3|(-1x^2 - 2x + 5) + 2|) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
4
|
math
|
algebra_func_zeros_train_0192
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = -3sin(2π((3(-5x + 4) - 1)/(1(-5x + 4))) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
18
|
math
|
algebra_func_zeros_train_0193
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many solutions does the equation 1(1(-1|(2cos(1πx + 1) - 2) - 3| + 3)^2 + 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
algebra_func_zeros_train_0194
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-1(1(-3(1|x + 3| - 1) - 1)^2 - 2(-3(1|x + 3| - 1) - 1) + 2) + 3)/(-3(1(-3(1|x + 3| - 1) - 1)^2 - 2(-3(1|x + 3| - 1) - 1) + 2) + 4) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0195
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2sin(3π(4(-2x^2 + 3x - 2) + 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
1088
|
math
|
algebra_func_zeros_train_0196
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = (-1(-1(-2x^2 + 5x - 4) - 4) + 2)/(2(-1(-2x^2 + 5x - 4) - 4) + 1) where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0197
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -2|(2(5x + 5)^2 - 4(5x + 5) + 5) - 3| + 3 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
2
|
math
|
algebra_func_zeros_train_0198
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "How many zeros does the function f(x) = 2(-3sin(3π(-4((-1x - 1)/(-2x - 3))^2 + 1((-1x - 1)/(-2x - 3)) + 1) - 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
46
|
math
|
algebra_func_zeros_train_0199
|
algebra_func_zeros
| null |
[
{
"role": "user",
"content": "Find the number of x-intercepts of the function f(x) = -1(-1((-2(2cos(1πx - 1) + 1))/(-1(2cos(1πx - 1) + 1) + 2)) + 5)^2 + 1(-1((-2(2cos(1πx - 1) + 1))/(-1(2cos(1πx - 1) + 1) + 2)) + 5) + 5 where -10 ≤ x ≤ 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}"
}
] |
20
|
math
|
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