Leafy palm trees are found only in the Kharazi Jungle. They are spaced sporadically around the jungle but have a fair concentration around the water pool, which is near teak trees marked by the western tree symbol
on the map. There is also one near the totem pole in the west of the jungle. This tree cannot be cut, but shaking one causes a palm leaf to drop out. Palm leaves can be used for cooking oomlie wraps which requires 50 cooking, and is one of the hard Karamja Tasks. There is a cool-down period of about 35 seconds before another leaf can be obtained from the same tree. To save a small amount of time on the Karamja Tasks, you can shake a leafy palm tree, then drop and pick up the leaf five times.
If you shake a leaf out of the tree, you get a message describing the tree as a "bamboo tree". This is an error, as bamboo is a grass and is unrelated to the palms.