Power-supply made of battery+solar cell, ultra low power
It is generally a diode OR circuit, a diode from the battery and a diode from the solar panel, when ever the solar panel has enough light, its voltage is higher than the batteries, so it stops it discharging and runs off only the panel, the earlier devices would also have a shunt regulator to keep the maximum solar panel voltage from getting too high, 

A more modern approach would be something like a power ORing IC, it monitors the voltages of both sources and switches to whichever is higher, and some of them can be quite low power, 

These calculators generally run on nano-amps, so the power lost through diodes is practically 0, as the voltage drop is much lower at these currents, you still get the same mAh capacity, just at a lower voltage that the device was already designed to run on, most IC's current does not change significantly with supply voltage.