Project Instructions: For this project you will create a Riemann sum calculator intended for use by another person $($a person not yourself$).$ The user $($not you$)$ should be able to enter their own function, bounds a and $b,$ and value of $n.$ The user will then obtain the following: left Riemann sum, right Riemann sum, midpoint Riemann sum, and trapezoidal Riemann sum.

Your sheet will likely need to make use of a macro to copy the user$-$entered function. You do not need to be concerned with error handling, as you may assume that the user will enter valid information for an integrable function on reasonable bounds. Your sheet should be able to handle any choice of real numbers for a and $b,$ and an integer value of $n$ up to $10,000.$

You may either $($a$)$ construct a sheet that displays only one of the four types at a time, with a switching mechanism for the different types, or $($b$)$ display all four simultaneously.

Your submission will contain both a working Excel file and a written document. If your sheet requires macros for full functionality, be sure to save the file as macro$-$enabled $(x|sm|)$ and not as a regular workbook $($xIsx$).$ Your written document should contain entirely verbal instructions $($if necessary$)$ for a user and a report of where you tested five completely different functions. These functions must be tested with different parameters $a,b,$ airid n$.$ No two functions should be tested with the same set of parameters. Please document your findings completely and verbally for all five functions.

Hint for Trapezoidal Rule: You will have $n$ trapezoids instead of $n$ rectangles for this approximation method. The area of a trapezoid is given by $\frac{H_1+H_2}{2}x,$ where $H_1$ is the height of the top left corner, $H_2$ is the height of the top right corner, and $x$ is the length of the base. In other words, base times the average height.