Programming the TI-Nspire CX CAS to implement Simpson's Rule is feasible and can be achieved by following specific steps. First, refer to the user manual for the correct syntax of the programming language. The program should prompt users for parameters such as $a$, $b$, $n$, and $f(x)$. An effective approach involves using a loop to evaluate the function at three successive points, maintaining a running sum throughout the process. After completing the loop, the sum should be multiplied by the appropriate constant from Simpson's Rule formula to produce the final output. Sharing pseudo-code for review can help refine the program and ensure accuracy.