# Crazy diffy! 3

Calculus Level 5

$\large \displaystyle \dfrac { da }{ db } ={ a }^{ 2 }+\int _{ 0 }^{ { \pi } / { 4 } }{ \left( { a }^{ 2 } \right) \, db }$

For the differential equation above, $$a=f(b)$$ and $$a(0)=0$$. Find $$\left\lceil a\left( 0.5 \right) \right\rceil$$.

Details and Assumptions: