$(7)$ Find function $F(x),F(x)={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(x^3+1)e^{x}dx($assign constant $C=0)$ and then calculate ${\displaystyle \underset{-5}{\overset{0}{}}}{F}^2(x)dx$ using Simpson's $\frac{1}{3}$ rule with $n=2(3$ points$).($approximate the results to two decimals$)$

$(8)$ Calculate the integral ${\displaystyle \underset{0}{\overset{1}{}}}\frac{1}{\sqrt[3]{x^5+7}}dx$ using trapezoidal rule and Simpson's $\frac{1}{3}$ rule with $n=4,$ respectively. Approximate the result to three decimals.