"No sign of movement. Looks like we've got the element of sur—"
—Gaiza, Mardu raider

Monastery Swiftspear

Haste
Prowess (Whenever you cast a noncreature spell, this creature gets +1/+1 until end of turn.)

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Any spell you cast that doesn't have the type creature will cause prowess to trigger. If a spell has multiple types, and one of those types is creature (such as an artifact creature), casting it won't cause prowess to trigger. Playing a land also won't cause prowess to trigger.

Once it triggers, prowess isn't connected to the spell that caused it to trigger. If that spell is countered, prowess will still resolve.

Prowess goes on the stack on top of the spell that caused it to trigger. It will resolve before that spell.

An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.