(a) Set up a double integral for calculating the flux of the vector field $\vec{F}(x,y,z) = \langle xz, yz, z^{4} \rangle$ through the open-ended circular cylinder of radius $8$ and height $4$ with its base on the xy-plane and centered about the positive z-axis, oriented away from the z-axis. If necessary, enter $\theta$ as theta.

Flux = $\displaystyle \int_{A}^{B} \!\! \int_{C}^{D}$ $dz \, d\theta$

A =
B =
C =
D =

(b) Evaluate the integral.
Flux = $\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A}$ =