These values are treated exactly the same as a value calculated from the STR score would.
Jump simply triples the jump distance - in the case of a frog, that would allow a 30 feet long jump and a 15 feet high jump. Or at least in theory - a frog only has 20 feet of movement, so that limits its long jump to 20 feet as well, unless something is increasing his speed, too.
Either way, this trait exists because otherwise, a frog with its STR score of 1 could make long jumps of only 1 foot, and high jumps of negative 2 feet. See the PHB, p. 182 for details.
Therefore, considering that frogs are not exactly bad at jumping, the developers presumably added this trait to compensate for the RAW low jump distance.
To summarize: all effects that modify jump distance that I know of modify the base jump value. The Standing Leap trait simply replaces the regular STR-based value with a fixed value and removes the requirement to move a certain distance before the jump. How the base value is calculated doesn't matter, unless a feature specifically modifies the STR-based jump distance. For example, the following effect would not benefit a frog:
Example spell or feature effect. For the purpose of calculating your jump distance, treat your STR score as twice its actual score.
I'm not aware of any feature that uses such a wording, though.