We present Quokka#, a versatile, open-source Python library for quantum circuit analysis. Quokka# reduces quantum circuit simulation, verification, and synthesis to (maximum) weighted model counting. It supports universal quantum circuits using nearly any gate set and provides performance trade-offs via encodings in different bases and through different encodings of equivalence checking. Quokka# enables both exact and approximate analysis approaches by computing the Jamiołkowski fidelity between circuits, which is essential for synthesizing circuits in different gate sets. This paper demonstrates the design of Quokka# and provides experimental evidence demonstrating the potential of this approach.