How do I sample a function using the metropolis algorithm?

f(x)=exp(-x/lambda)*1/lambda

Write a program to sample f(x) by the Metropolis algorithm. Start from any position you like. Equilibrate the random walk for several hundred steps before collecting samples. After equilibration, divide the random walk into n_mea blocks of n_smpls_per_mea each.

[Walter Roberson]

Is that the Metropolis-Hastings algorithm ?

Presumably you were given a reference to the required algorithm in class or in one of the texts for the class.