Lindsay Lohan -- I Showed Troubled Youth The Right Path ... and I Got Credit!

Lindsay Lohan got credit for 18 hours of community service for doing meet and greets with fans who went to see her London play ... and that's why the prosecutor is furious.

It's pretty stunning ... Community Service Volunteers in London submitted docs to the court in Lindsay's probation case Wednesday ... listing 5 meet and greets following her performances in "Speed-the-Plow." According to the docs, each hangout lasted 3 HOURS!

But wait ... it gets even more bizarre ... CSV gave 5 lucky probationers a total of 70 hours with Lindsay ... providing them with "work shadowing experience." In other words, young people who needed to be taught a lesson followed Lindsay by way of example. The other thing ... she's not even working right now.

Prosecutor Terry White wants 2 weeks to get to the bottom of it before he makes a recommendation to the judge. Lindsay's lawyer, Shawn Holley, told the judge Lindsay merely complied with CSV rules.