As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school. But there are five other Astika or orthodox schools of Hindu philosophy: Purva Mimamsa, Samkhya, Yoga, Vaisheshika, and Nyaya. My question is about the Samkhya school, founded by the sage Kapila. Now in Adhyaya 4 of Kapila's Samkhya Sutras, one of the defining texts of the Samkhya school, Kapila discusses various scriptural stories which illustrate different Samkhya teachings. In particular, here's what he says in Adhyaya 4 Sutra 16:
In the forgetting also of the rules (there is the same harm), as (in the story of) the she-frog.
Here's how Aniruddha interprets this Sutra in his commentary on the Samkhya Sutras:
The author tells us that by reason of the forgetting of the knowledge of the Principles, pain necessarily takes place. A certain king, going out on a hunting excursion, saw a beautiful maid in the woods. He asked her, "Who are you?" "I am a king's daughter," replied she. The king said, "Marry me." "Very well," said she, "but make this rule that water must not be shown to me by you." "Let it be so," - so saying, he took her hand. In this manner, as time went on, one day, she, being fatigued with sport, asked the king "Where can I get water from?" The king, too, forgetting his promise, through haste, showed her water. And she, who was the daughter of the king of frogs, was, through touch of water, transformed as a she-frog. The king, on the other hand, searching for her by means of nets, etc. and, not regaining her, experienced much pain. Therefore, interruption of the cultivation of the Principles should not be made.
My question is, what scriptures describe this story of a king who fell in love with a frog princess?
This story is interesting for two reasons. First of all, it's reminiscent of the story of Shantanu and Ganga, in that a wife places a condition that the husband breaks. Second of all, it reminds me of the European story of the Frog Prince. In fact, it's kind of the mirror image of that story. In the Frog Prince, a princess keeps a promise to a male frog, and thereby it turns into a human. In this story, a king breaks a promise to a female human, and thereby she turns into a frog.