$($a$)$ Set up a double integral for calculating the flux of the vector field vec$(F)(x,y,z)=$yvec$(i)+7$vec$(j)-$xzvec$(k)$ through the part of the surface $y=x^2+z^2$ for $0y11,$ oriented in the positive $y-$direction.

Flux $={}_{\text{D}\text{i}\text{s}\text{k}}dxdz$

$($b$)$ Evaluate the integral.

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