In the vanguard of neuromorphic engineering, we develop a paradigm of biocompatible polymer memcapacitors using a seamless solution process, unleashing comprehensive synaptic capabilities depending on both the stimulation form and history. Like the human brain to learn and adapt, the memcapacitors exhibit analogue-type and evolvable capacitance shifts that mirror the complex flexibility of synaptic strengthening and weakening. With increasing frequency and intensity of the stimulation, the memcapacitors demonstrate an evolution from short-term plasticity (STP) to long-term plasticity (LTP), and even to metaplasticity (MP) at a higher level. A physical picture, featuring the stimulus-controlled spatiotemporal ion redistribution in the polymer, elaborates the origin of the memcapacitive prowess and resultant versatile synaptic plasticity. The distinctive MP behavior endows the memcapacitors with a dynamic learning rate (LR), which is utilized in an artificial neural network. The superiority of implementing a dynamic LR compared with conventional practices of using constant LR shines light on the potential of the memcapacitors to exploit organic neuromorphic computing hardware.