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Maybe Maxwell was trying to figure out how he could attack the Cardassians and came across Commodore Decker's old musings on how to dispose of troublesome crew members.
Kirk first tries simply barging in. Then he tries getting past the cube. Only after hours of failing to achieve that does he try "a spiral course away from the cube", but only because doing nothing would make Kirk appear too weak.
That spiral course involves the cube "still blocking" and Kirk musing if it will "give way", so it sounds very much like another attempt at getting past the thing, not a retreat. Naturally the cube then gives chase, matching Kirk's warp three before Kirk fires.