If the value of the integral $\int_0^5 \frac{x+[x]}{e^{x-[x]}} d x=\alpha e^{-1}+\beta$, where $a, b \in R, 5 \alpha+6 \beta=0$, and $[x]$ denotes the greatest integer less than or equal to $x$; then the value of $(\alpha+\beta)^2$ is equal to :
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