Let vec$(H)=(e^{xy}+7z+5)vec(i)+10$vec$(j)+(7z+e^{xy})vec(k).Sis$ the square $of$ side $6on$ the plane $z=x$ oriented downward.

$(a)$ Find

$(b)$ Set $up$ and find the flux $of$ vec$(H)$ through $S.$

${\displaystyle \underset{S}{\overset{\phantom{}}{}}}$vec$(H)*dvec(A)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$

$\sqrt[\phantom{2}]{?}$