Write two user written functions to perform numerical integration using the trapezoid method and Simpsons One Third Method, which you will name trap_method and Simpsons_1_3 respectively. Your function must accept the following arguments for both functions: an independent vector of numbers and a dependent vector of numbers. Your function file must perform the following tasks:

1. Check that both vectors are of equal length.
2. Check that the independent vector in the Simpsons Method has equal spaced intervals.
3. Compute numerically using trapezoid method and return the value of the integral.
4. Compute numerically using Simpsons One Third method and return the value of the integral.