The play vs Computer is still here under Play > Computer. If you want a custom position, you need use Learn > Analysis, set up your position and then click the Finish vs Computer option 
playing set positions against the computer
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Is it possible in new chess. com to play-out set positions against the computer. For example to checkmate a lone king against two bishops on squares with opposite colours. I think that In old chess.com it used to be called 'play the computer'. Regards, David