Perform shell operation through secure shell

Is it possible to perform a shell operation from a bash script through a secure shell.

Here is an example of why you may want to do this. Lets say you have a simple unix operating system that you need only build and run on, but you want to do all of the development on another machine. I want to write a bash script that has the following functionality:

scp file to location on other machinessh to other machinecd into correct directory make run programscp results to file on original computerexit ssh

Is this remotely possible? (Pardon the Pun :p)