Every day, Naranath starts from the bottom of a valley and pushes his boulder all the way up to the summit of a mountain. He then lets it roll all the way back down the mountain and laughs thunderously.

\[f(x) = \cos^5(x) + 1, x \in [-\pi, \pi]\]

...represents the height of the mountain at a given point. How far does the boulder roll every day?

**Details and assumptions:**

- The boulder stops as soon as it hits the bottom of the valley; it doesn't roll any further.
- Round to the hundredth's place.

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