A square has sides of length $10$, and a circle centered at one of its vertices has radius $10$. What is the area of the union of the regions enclosed by the square and the circle? Express the area in the form $a + b\pi$, where $a$ and $b$ are constants. Please find the value of x + y, where a = x and b = y.

Let's think step by step and output the final answer within \boxed{}.
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