Okay, so the question specifies to use Stokes' theorem to evaluate the flux integral
$$\iint\limits_{S} \text{curl}( \boldsymbol{F}) \cdot\ \boldsymbol{N}dS \; \text{where}\; \boldsymbol{F} = \langle \cos z + 4y \rangle i+ \langle \sin z + 4x \rangle j + \langle x^{2}z^{2} \rangle k$$ and $S$ is part of the surface $z = 9-x^{2} -y^{2}$ and $z\geq0$ and $N$ points upward.
I am failing to see a way to solve this problem using a simple method. The correct answer is $0$, but I am not seeing a way that this could be done using any simple method. Is there some type of simplification that I am missing?
Thanks!