As for whether they will leave the terrarium, as others have said, it likely depends on the frog. I had a gray treefrog (Hyla chrysoscelis/versicolor) in an 18 gallon and mistakenly left the lid off one day. I came home to find him perched on the lip of the tank, but that is as far as he went.
It all depends on your definition of intelligence. Amphibians are not self-aware, as are dolphins or apes. But many are capable of intriguing behaviors, such as natal site fidelity (wherein an individual returns to the same pond from which it emerged as a metamorph). Their homing abilities have been well studied, and these studies demonstrate that amphibians are at least able to use a mental map. However, as for problem solving, they fall behind many other vertebrates. As for feeding behaviors, such as equating humans with food, I would argue that it simply demonstrates their ability to adapt and react within the confines of their world. For a large part, it's learning based on conditioning. For example, my larval Eurycea, named Guano, recognizes that I mean food. He will follow me as I move around the tank. It has also as learned that food (frozen bloodworms) comes from above, and will arch its back or prop itself up when hunting. Another example is "fence-stalking" in snakes. When researchers employ drift-fences to study herp (reptile and amphibian) populations, local snakes can learn to stalk the fence and eat any critters that fall in the pits. Because they have always, or at least frequently, encountered food items at the fence, the fence becomes associated with food.





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