# 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 \( (a + b + k)^{12} \).