A surface $S$ has a parametrization $(u,v),$ whose domain $D$ is the square shown in the figure.

Suppose that $$ has the following normal vectors

$N(A)=($:$3,1,0$:$),N(B)=($:$1,6,0$:$)$

$N(C)=($:$5,0,1$:$),N(D)=($:$3,0,1$:$)$

Estimate ${}_{S}f(x,y,z)dS,$ where $f$ is a function such that $f((u,v))=u+v.$

$($Use decimal notation. Give your answer to three decimal places.$)$

${}_{S}f(x,y,z)dS$~~