The IceCube South Pole Neutrino Observatory has discovered the presence of a diffuse astrophysical neutrino flux at energies of TeV and beyond using neutrino induced muon tracks and cascade events from neutrino interactions. We present two analyses sensitive to neutrino events in the energy range 1 TeV to 10 PeV, using more than 10 years of IceCube data. Both analyses consistently reject a neutrino spectrum following a single power-law with a significance of >4σ in favor of a broken power law. We describe the methods implemented in the two analyses, the spectral constraints obtained, and the validation of the robustness of the results. Additionally, we report the detection of a muon neutrino in the medium energy starting events sample, or MESE, with an energy of 11.4+2.46-2.53 PeV, the highest energy neutrino observed by IceCube to date. The results presented here show insights into the spectral shape of astrophysical neutrinos, which has important implications for inferring their production processes in a multimessenger picture.