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The MODE key is for setting the angular mode. The current angular mode is shown using one of the symbols D, R or G at the far right of the display.
It has auto power-off. Memory is not retained when the calculator is in the auto power-off state. To switch it back on press the AC key.
This calculator (as do many other CASIO scientific calculators) uses one and the same key for both the constant π as well as exponents. This works as follows. When you first enter digits, the EXP key will enable you to enter the exponent, otherwise it will enter the constant π.