Use the Divergence Theorem to calculate the surface integral $ \iint_S \textbf{F} \cdot d\textbf{S} $; that is, calculate the flux of $ \textbf{F} $ across $ S $.
$ \textbf{F}(x, y, z) = (2x^3 + y^3) \, \textbf{i} + (y^3 + z^3) \, \textbf{j} + 3y^2z \, \textbf{k} $,
$ S $ is the surface of the solid bounded by the paraboloid $ z = 1 - x^2 - y^2 $ and the $ xy $-plane