Evaluate the surface integral using Stokes' Theorem

${}_S$curl$(vec(F))*dvec(S),$

where vec$(F)(x,y,z)=(x^2+y-4,3xy,2xz+z^2)$ and $S$ is the upper hemisphere $x^2+y^2+z^2=16,z0$ with positive $($outward$)$ orientation.