Capacitor with op-amp
In the ideal sense, that capacitor will hold its charge for a very long time because of the high input impedance of the FET input opamp, and slowly leak to ground.  In reality, the circuit probably isn't very useful, as the bias current from the positive input of the amplfier has nowhere to go but that capacitor, so your amplifier output will probably eventually saturate at the positive or negative rail, depending on the direction of the bias current.