ABSTRACT: Numerical continuation is the process of solving systems of nonlinear parameter dependent equations for various parameter values. Continuation studies are often helpful in understanding changes in a physical or natural system.  In particular, as a fluid changes density or temperature, one can observe crucial transitions in structural and thermodynamic properties.  In this talk, I present new integral equation theory for atomic and molecular fluids developed at the Institute for Molecular Design at the University of Houston.  Further, I discuss a new  implementation of this theory in the context of numerical continuation using Trilinos, a software framework developed at Sandia National Labs.