We present a measurement of the high-energy astrophysical muon-neutrino flux with the IceCube Neutrino Observatory. The measurement uses a high-purity selection of ~650k neutrino-induced muon tracks from the Northern celestial hemisphere, corresponding to 9.5 years of experimental data. With respect to previous publications, the measurement is improved by the increased size of the event sample and the extended model testing beyond simple power-law hypotheses. An updated treatment of systematic uncertainties and atmospheric background fluxes has been implemented based on recent models. The best-fit single power-law parameterization for the astrophysical energy spectrum results in a normalization of $ϕ_{\mathrm{@100TeV}}^{ν_μ+\barν_μ} = 1.44_{-0.26}^{+0.25} \times 10^{-18}\,\mathrm{GeV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}\mathrm{sr}^{-1}$ and a spectral index $γ_{\mathrm{SPL}} = 2.37_{-0.09}^{+0.09}$, constrained in the energy range from $15\,\mathrm{TeV}$ to $5\,\mathrm{PeV}$. The model tests include a single power law with a spectral cutoff at high energies, a log-parabola model, several source-class specific flux predictions from the literature and a model-independent spectral unfolding. The data is well consistent with a single power law hypothesis, however, spectra with softening above one PeV are statistically more favorable at a two sigma level.