The part number you need is 41C4220A and is available at any good door opener service company. It comes with instructions. Don't take any shortcuts. This situation usually occurs when the opener is lifting a door that hasn't been properly maintained and is need of new springs. Try releasing it from the opener and operating by hand. It should not be heavy and should stay in place when released about waist to shoulder high.

every gear inside the motor housing looks great with no shavings accumulated or abnormal wear. I have inspected the door rollers and found one to have worked the mounting screws loose. I am wondering if during the last close cycle this roller somehow wedged enough causing excess torque on the motor and resulting in the sprocket shaft twisting/snapping. It is a clean break just at the point where the sprocket meets the housing.

That assembly has a bronze bearing the shaft runs through. A heavy door causes the bearing to wear and lets the shaft rub against the steel cover and cuts the shaft to the point where it breaks. I have never seen a shaft break from other causes but I suppose. Check the door balance.