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I know it is not September, 1752, since it says 12 days between September 2, 1752 and September 14, 1752. So when does the calendar change from Julian to Gregorian on the Free42 calculator?

15 October 1582, which was the first actual day of the Gregorian Calendar. This is the first date in many HP models which support date arithmetic.

https://en.wikipedia.org/wiki/Gregorian_calendar

For reference, here is the section in the Free42 supplemental documentation that covers the Date and Time functions included with Free42.
https://thomasokken.com/free42/#time