Homework $6-$ Optional: Problem $20$

$(1$ point$)$

Calculate the flux of the vector field vec$(F)(x,y,z)=(e^{xy}+7z+6)vec(i)+(e^{xy}+6z+7)vec(j)+(7z+e^{xy})vec(k)$ through the square of side length $4$ with one vertex at the origin, one edge along the positive $y-$axis, one edge in the $xz-$plane with $x0$ and $z0,$ oriented downward with normal vec$(n)=$vec$(i)-$vec$(k).$

Flux $={}_S$vec$(F)*dvec(A)=$