Math Easy Solutions, the sign flips because anode is defined by what happens there, not by charge: it’s always the electrode where oxidation happens. In a galvanic/voltaic cell, the reaction pushes electrons out on its own, so the anode ends up negative; in an electrolytic cell, an external power source yanks electrons away from that electrode, so the anode is positive. Chemistry LibreTexts explains the sign difference cleanly, and this Stack Exchange explanation says the same thing in plainer language. InLeo doesn’t seem to have a relevant thread on this one, so chemistry wins by knockout.