The easiest way to "program" the Emacs Calculator is to use standard keyboard macros. Press C-x ( to begin recording a macro. From this point on, keystrokes you type will be saved away as well as performing their usual functions. Press C-x ) to end recording. Press shift-X (or the standard Emacs key sequence C-x e) to execute your keyboard macro by replaying the recorded keystrokes. See section `Keyboard Macros' in the Emacs Manual, for further information.
When you use X to invoke a keyboard macro, the entire macro is
treated as a single command by the undo and trail features. The stack
display buffer is not updated during macro execution, but is instead
fixed up once the macro completes. Thus, commands defined with keyboard
macros are convenient and efficient. The C-x e command, on the
other hand, invokes the keyboard macro with no special treatment: Each
command in the macro will record its own undo information and trail entry,
and update the stack buffer accordingly. If your macro uses features
outside of Calc's control to operate on the contents of the Calc stack
buffer, or if it includes Undo, Redo, or last-arguments commands, you
must use C-x e to make sure the buffer and undo list are up-to-date
at all times. You could also consider using K (calc-keep-args)
instead of M-RET (calc-last-args).
Calc extends the standard Emacs keyboard macros in several ways. Keyboard macros can be used to create user-defined commands. Keyboard macros can include conditional and iteration structures, somewhat analogous to those provided by a traditional programmable calculator.