Evaluate : `int_(0)^(pi) |cos x| dx`

Explanation

To evaluate the integral \( I = \int_{0}^{\pi} |\cos x| \, dx \), we will break it down into two parts based on the behavior of the cosine function.

### Step 1: Identify the intervals
The function \( |\cos x| \) behaves differently in the intervals \( [0, \frac{\pi}{2}] \) and \( [\frac{\pi}{2}, \pi] \):
- In the interval \( [0, \frac{\pi}{2}] \), \( \cos x \) is non-negative, so \( |\cos x| = \cos x \).
- In the interval \( [\frac{\pi}{2}, \pi] \), \( \cos x \) is non-positive, so \( |\cos x| = -\cos x \).

### Step 2: Break the integral into parts
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