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Obviously, there is a boundary curve at the middle of this cube that goes around the 4 sides, front, right, back, and left.

This boundary curve forms the boundary of the top half of the cube with the 5 faces and the bottom half of the cube with the 4 faces(bottom face is missing)

Does STOKE's theorem break apart here? The curl of the field dot the 5 faces of the cube ought to equal the closed boundary line integral... But I am missing the bottom face of the cube.

HELP