Compute ${}_{S}F*dS,F=($:$0,0,z^2$:$),$ for the oriented surface $S$ parametrized by

$(u,v)=(ucos(v),$usin$(v),v),0u3,0v2,$ with the upward$-$pointing normal.

$($Use symbolic notation and fractions where needed.$)$

${}_{S}F*dS=$