# Catch me if you can!

Calculus Level 4

$\large \int_0^\pi e^{\cos \theta} \cos (\sin \theta) d \theta$

The above definite integral evaluates to a number of the form $$a \pi^b + k$$ where $$a$$ , $$b$$ and $$k$$ are integers. Find the sum of the digits of the number $$(a + b + k)^{12}$$.

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