Evaluate `int_(-pi//4)^(pi//4)x^(3)sin^(2)xdx`

Explanation

To evaluate the integral \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} x^3 \sin^2 x \, dx \), we will check whether the integrand is an odd function or an even function.

### Step 1: Identify the function
Let \( f(x) = x^3 \sin^2 x \).

### Step 2: Check if the function is odd or even
To determine if \( f(x) \) is odd or even, we need to evaluate \( f(-x) \):
\[
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