How to shift distributions using built in functions?

I want to use built in functions to shift distributions. For example: instead of the exponential distribution F(x)=1-exp(-a*x),x>0, I want to shift the function with a parameter b to get F(x)=1-exp(-a*(x-b)), so now the distribution exists for x>b. Of course I can just type it out in Matlab but for more involved distributions it becomes more prone to errors and just maybe unnecessary work. I would like to know how I can make the shifted distribution using

 x=0:0.1:100;
 f=makedist('Exponential','mu',a)
 F=cdf(f,x)

or

 x=0:0.1:100; 
 F=expcdf(x,a)

or something similar to include the parameter b. Any solution involving symbolic variables is also fine as long as it does not involve typing out entire distributions. I am more interested in the cumulative distribution function than the probability density function, just in case there would be any integration involved in the answer.