"I would like to learn not to look in the box."
Translation:Jeg vil gerne lære ikke at kigge i kassen.
I might be wrong about this one but could it possibly be the same trick as in "Jeg tror ikke at han kommer" rather than "Jeg tror at han ikke kommer"? A possible explanation would be that in Danish the main verb is the one that takes the negative form, rather than the secondary. Just my five cents though...