We construct a model of quintessential inflation in Palatini $R^2$ gravity
    employing a scalar field with a simple exponential potential and coupled to
    gravity with a running non-minimal coupling. At early times, the field acts as
    the inflaton, while later on it becomes the current dark energy. Combining the
    scalar sector with an ideal fluid, we study the cosmological evolution of the
    model from inflation all the way to dark energy domination. We interpret the
    results in the Einstein frame, where a coupling emerges between the fluid and
    the field, feeding energy from the former to the latter during the
    matter-dominated era. We perform a numerical scan over the parameter space and
    find points that align with observations for both the inflationary CMB data and
    the late-time behaviour. The final dark energy density emerges from an
    interplay between the model parameters, without requiring the extreme
    fine-tuning of the cosmological constant in $\Lambda$CDM.

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