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Based on a 6 cm-long two-segment hybrid capillary discharge waveguide, a multi-GeV electron beam with energy up to 3.2 GeV and 9.7% rms energy spread was achieved in a cascaded laser wakefield acceleration scheme, powered by an on-target 210 TW laser pulse. The electron beam was trapped in the first segment via ionization-induced injection, and then seeded into the second segment for further acceleration. The long-distance stable guiding of the laser pulse and suppression of the dark current inside the second-segment capillary played an important role in the generation of high-energy electron beams, as demonstrated by quasi-three-dimensional particle-in-cell simulations.