When riding my bike uphill, downhill, and flat; I try to make it where I can continue keeping my breath. So, I like to stay at an average power. Lowering the power output is also a way of keeping my breath.

In all of your cases, torque and angular velocity of the pedal is not changing which means that you expect power to change because you are cycling through the gear train. This will keep a constant linear velocity, but will put the cyclist out of breath quickly because the load may be much larger and power must be increased.

In my case, I expect the rider's linear velocity to vary quite dramatically between flat and uphill. A constant applied power will do just this because of the varying loads.

Either way, you have been correct early in your posts, but it seems that we may have a communication problem. For example, a constant RPM in all three cases being the same RPM or different RPMs that are held at a constant rate. I think subscripts would be very helpful in this case.