The method can easily be implemented numerically through the following simple algorithm

• Choose the number of mesh points and fix the step.
• calculate $f(a)$ and $f(b)$
• Perform a loop over $n=1$ to $n-1$ ($f(a)$ and $f(b)$ are known) and sum up the terms $4f(a+h) +2f(a+2h)+4f(a+3h)+\dots +4f(b-h)$. Each step in the loop corresponds to a given value $a+nh$. Odd values of $n$ give $4$ as factor while even values yield $2$ as factor.
• Multiply the final result by $\frac{h}{3}$.