Maytag washer tub spins during agitate.

When in agitate cycle, the tub slowly starts spinning ,gradually getting faster, so fast that water sloshes out of the tub. This spinning is the opposite direction from the spin cycle. With the front removed, I can brace the transmission with my foot before it starts spinning and if I hold it there it will agitate fine. Is this a transmission problem, or is there something else (brake?) that could be the cause?

You have a bad brake. AP4373089
This also requires the purchase of a special tool: [part]AP3856708[/part]