Project defined functions

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I guess your question is referring to a CoCalc project. Then, it suffices to place the definition of the function in the file .sage/init.sage in the home directory of the project.

You can do this, for instance, by clicking on Filesin the top menu bar, then click on the "eye" button on the top right (just at the left of the Backups button). The subdirectory .sage will then show up in the list; click on it and then click on init.sage to open it. You can enter the code of the function there and save it. As an example, if you type the following two lines in that file:

def f(x):
    return x^2

the function f will be available in any Sage session of the project.