Answer
$61$
Work Step by Step
We expand and simplify the sum:
$\displaystyle \sum_{i=0}^{4}(2^{i}+i^{2})$
$=(2^0+0^2)+(2^1+1^2)+(2^2+2^2)+(2^3+3^2)+(2^4+4^2)$
$=(1+0)+(2+1)+(4+4)+(8+9)+(16+16)$
$=61$
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