Calculate ${}_S$vec$(F)*dS$ where

vec$(F)=($:$4x^{3}z,4y^{3}z,3z^4$:$)$

and $S$ is the surface of the solid bounded by the hemispheres $z=\sqrt[\phantom{2}]{25-x^2-y^2},z=\sqrt[\phantom{2}]{4-x^2-y^2}$ and the plane $z=0.$

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