Calculate the equations in "Introduction to Probability Models" 11th editon, section 2.3.2:
$$ F(a) = \int_0^a \lambda e^{-\lambda x} dx \qquad a \ge 0, \lambda > 0 $$
$$ \int_0^\infty \lambda e^{-\lambda x} dx \qquad \lambda > 0 $$
WolframAlpha
Integral from 0 to a:
Integrate[\[Lambda] e^(-\[Lambda] x), {x, 0, a}]
Integral from 0 to infinity:
Integrate[\[Lambda] e^(-\[Lambda] x), {x, 0, Infinity}].
With assumptions:
Integrate[\[Lambda] e^(-\[Lambda] x), {x, 0, Infinity}, assumptions -> \[Lambda] > 0].
Or put assumptions outside the expression:
assuming[\[Lambda] > 0, Integrate[\[Lambda] e^(-\[Lambda] x), {x, 0, Infinity}]].
Sympy
from sympy import integrate, oo, exp, init_printing
from sympy.assumptions import assuming
from sympy.abc import x, lamda, a
init_printing()
with assuming(a >=0, lamda >0):
res1 = integrate(lamda * exp(-1 * lamda * x), x)
res2 = integrate(lamda * exp(-1 * lamda * x), (x, 0, oo))
The display effect of math equations in jupyter notebook is better then in ipython console.
SageMath
%var x, lmd
assume(lmd > 0)
integral(lmd * exp(-1*lmd*x),x)
integral(lmd * exp(-1*lmd*x),x, 0, oo)
No time to implementations in Maxima today.