A contour map is shown for a function $f$ on the square $R=[0,6][0,6].$

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$($i$)$

$($a$)$ Use the Midpoint Rule with $m=n=2$ to estimate the value of ${}_{R}f(x,y)dA.($Round your answer to the nearest integer.$)$

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$($b$)$ Estimate the average value of $f.($Round your answer to one decimal place.$)$