The time period of a pendulum confined in a vertical plane is given by

$T=4\sqrt[\phantom{2}]{\frac{l}{2g}}{\displaystyle \underset{0}{\overset{{}_0}{}}}\frac{d}{\sqrt[\phantom{2}]{cos-cos{}_0}}$

where ${}_0$ is the maximum of the angle between the pendulum and the downward vertical, $l$ is the length of the pendulum, and $g$ is the acceleration due to gravity. Write a Fortran code to evaluate this integral using Simpson's $\frac{1}{3^{rd}}$ rule for ${}_0=10$ to $90$ in step of $10$ and compare each result with the small$-$ angle approximation $T$~~$2\sqrt[\phantom{2}]{\frac{l}{g}}.$ Take $l=g.$