Evaluate: `int_(-(3pi)/2)^(-pi/2)[(x+pi)^3+cos^2(x+3pi)]dx`

Explanation

To evaluate the integral

\[ I = \int_{-\frac{3\pi}{2}}^{-\frac{\pi}{2}} \left[(x + \pi)^3 + \cos^2(x + 3\pi)\right] dx, \]

we will follow these steps:

...