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We present the baseline conceptual design of the Cassegrain U-Band Efficient Spectrograph (CUBES) for the Very Large Telescope. CUBES will provide unprecedented sensitivity for spectroscopy on a 8 – 10 m class telescope in the ground ultraviolet (UV), spanning a bandwidth of ≥ 100 nm that starts at 300 nm, the shortest wavelength accessible from the ground. The design has been optimized for end-to-end efficiency and provides a spectral resolving power of R≥ 20000, that will unlock a broad range of new topics across solar system, Galactic and extraglactic astronomy. The design also features a second, lower-resolution (R ∼ 7000) mode and has the option of a fiberlink to the UVES instrument for simultaneous observations at longer wavelengths. Here we present the optical, mechanical and software design of the various subsystems of the instrument after the Phase A study of the project. We discuss the expected performances for the layout choices and highlight some of the performance trade-offs considered to best meet the instrument top-level requirements. We also introduce the model-based system engineering approach used to organize and manage the project activities and interfaces, in the context that it is increasingly necessary to integrate such tools in the development of complex astronomical projects. [ABSTRACT FROM AUTHOR]