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Neutrinos offer a unique window to the distant, high-energy universe. Several next-generation instruments are being designed and proposed to characterize the flux of TeV--EeV neutrinos. The projected physics reach of the detectors is often quantified with simulation studies. However, a complete Monte Carlo estimate of detector performance is costly from a computational perspective, restricting the number of detector configurations considered when designing the instruments. In this paper, we present a new Python-based software framework, toise, which forecasts the performance of a high-energy neutrino detector using parameterizations of the detector performance, such as the effective areas, angular and energy resolutions, etc. The framework can be used to forecast performance of a variety of physics analyses, including sensitivities to diffuse fluxes of neutrinos and sensitivity to both transient and steady state point sources. This parameterized approach reduces the need for extensive simulation studies in order to estimate detector performance, and allows the user to study the influence of single performance metrics, like the angular resolution, in isolation. The framework is designed to allow for multiple detector components, each with different responses and exposure times, and supports paramterization of both optical- and radio-Cherenkov (Askaryan) neutrino telescopes. In the paper, we describe the mathematical concepts behind toise and provide detailed instructive examples to introduce the reader to use of the framework.