Calculus is a fundamental subject in mathematics and extensively used in physics and astronomy. Performing calculus operations by analog computing has received much recent research interest because of its high speed and large data throughput; however, current analog calculus frameworks suffer from bulky sizes and relatively low integration densities. In this work, we introduce the concept of an epsilon-near-zero (ENZ) metamaterial processing unit (MPU) that performs differentiation and integration on analog signals to achieve extreme miniaturization at the subwavelength scale by generating desired dispersions of the ENZ metamaterials with photonic doping. To show the feasibility of this proposal, we further build an experimental analog image edge extraction system with a differentiating ENZ-MPU as its compute core. With a computing density theoretically analyzed to be several tera-operations per second and square micrometer, the proposed ENZ-MPU is scalable and configurable for more complex computations, providing an effective solution for analog calculus operators with extreme computing density and data throughput.