At a slightly simplistic level the propeller is a wing airfoil. However, even though it is a fixed pitch, the angle of attack varies with the true airspeed and RPM.
The thrust produced is basically the same angle of attach *True speed (in this case it is the sum of the speed due to rotation and forward advance)*density relationship as a wing, but with an additional variable. The efficiency is dependent on the difference between the inflow and outflow airspeed (which is why static thrust is lower than one might expect).
The power is then this rather complicated thrust * True Airspeed.
I suspect it is much easier to take some values from the POH and draw curves fitting the datapoints.