Thank you Flecc, I found this very helpful, indeed.
However, I am not clear about what pedaling strategy to employ when attempting to maximize my range on a hilly ride.
I presume the maximum range is obtained by simply turning off the motor

but I would like some assist up some of the hills. Should I drop into the lowest gear and pedal as slowly as I can (thus saving my bio mechanical energy) or should I shift into the highest gear and pedal as quickly as I can which would be quite slow, of course, but would this save my stored electromechanical energy?
Would my battery last longer if I pedaled slowly up hills in my lowest gear or pedaled slowly up hill in the highest gear I can manage?
Thanks.