The heat flow vector field for conducting objects is $F=-$kgradT, where $T(x,y,z)$ is the temperature in the object and $k$ is a constant that depends on the material. Compute the outward $f$ of F across the surface S for the given temperature distribution. Assume $k=1.$

$T(x,y,z)=90e^{-x-y}$; S consists of the faces of the cube $|x|3,|y|3,|z|3.$

The outward flux is

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