For the mathematically inclined, the algorithm simply evaluates an eighth-degree polynomial approximation of the cumulative density function at the two endpoints and subtracts. The polynomial approximation is based on mutually orthogonal polynomials on [-4.5,4.5]. The truth is, using the built in integrator on the formula for the normal curve is faster; this was an interesting experiment, though.
Just enter this program in your TI-82 and run.
You can download a binary version for linking to your calculator...
...or type in the program below.
If you type, please proofread your typing carefully; being off by just one character will likely cause serious errors.
Note that uppercase and lowercase are NOT interchangeable.