First starting out? No. Learn the form correctly first.
And as a newbie to weight training, you're liable to gain muscle mass and strength whatever the hell you do, so going to failure is kind of pointless. "Neural learning" or something. Take advantage of it. But you don't want to learn bad mistakes that you'll have to unlearn down the road.
(And for god's sake; if the trainer tells you that the proper form for a squat is on a Smith machine and keeping your back perfectly vertical, he's off his rocker.)
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