This is not a question. I just uploaded this problem for the posting.
If you evaluate $\displaystyle{\int_{S}\text{curl} \mathbf{F}\cdot d\mathbf{\sigma} }$ where $\displaystyle{ \mathbf{F} = \langle {\rm{exp}}(xz) +2y{\rm{exp}}(x^2+y^2) , {\rm{ln}} (\pi+{\rm{exp}}(y^{2n+1})) +3x {\rm{exp}}(x^2 +y^2), 3x^2 y \rangle }$ and $S$ is a positively oriented surface defined by $z=1-x^2 - y^2 , ~x^2+y^2 \le 1$ and $n\in \mathbb{N}$, then you can have $\displaystyle{\int_{S}\text{curl} \mathbf{F}\cdot d\mathbf{\sigma} }=\pi^a e^b$. Now, find $2000a+30b$.