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Wide-range energy measurements have been carried out with an encapsulated 36-fold segmented germanium detector of AGATA (Advanced GAmma-ray Tracking Array). An unprecedented equivalent energy range of 5 keV to 180 MeV, or ~90 dB, has been obtained using a single acquisition chain, while maintaining a high energy resolution in the whole spectrum. For energies larger than 3 MeV the pulse-height is obtained with a Time- over-Threshold (ToT) technique. The measured resolution in all the tested range from 3 to 50 MeV is of <0.4%. The ToT technique has been demonstrated using a 241Am + Be source with Ni target generating high-energy gamma photons by neutron capture reactions. A remarkable resolution of 0.21% has been obtained on the Ni spectrum line at the energy of 8.998 MeV.