The development of advanced software tools for power system analysis requires extensive programming expertise. Even when using open-source tools, programming skills are essential to modify built-in models. This can be particularly challenging for domain experts who lack coding proficiency. This paper introduces modelSolver, a software solution with a new framework centered around symbolic mathematical modeling. The proposed paradigm facilitates defining models through intuitive mathematical expressions, thus eliminating the need for traditional programming constructs such as arrays, loops, and sparse matrix computations. The modelSolver focuses on power flow and state estimation using an open-box approach, which allows users to specify custom models using either real or complex variables. Unlike existing tools that rely on hard-coded models, modelSolver enables the representation of a wide range of advanced functionalities, including power flow with voltage regulators and load tap changers, continuation power flow, and Gauss-Newton state estimation with equality constraints. Compatibility with MATPOWER is ensured via a converter that automates importing data files. The framework prioritizes model-driven development and empowers domain experts to focus on power system modeling without programming barriers. It aims to simplify power system computations, making them more accessible to students, scientists, and practitioners.