Question: How can I see, if the result of numeric integration is correct?

Dear Maple Primes,

could you, please, help me with numeric integration? I’m new in numeric integration and can’t reach desired precision of a result.
Here is the integral f(x_max) that I try to compute for different values of x_max from the interval 0.025..0.24 :

f:=(xmax)->Int(K*F*Int(G*F,x=x..xmax,method=integrationmethod),x=x0..xmax,method=integrationmethod)

where x₀ is lower limit of outer integral, x₀ := 0.025

and K, F and G are functions of x

K:=x-x0

F:=(a₁+a₂*x+a₃*x²+a₄*x⁵)/(b₁*x+b₂*x²+b₃*x⁶)

G:=exp(c₁+c₂*x+c₃*x⁷)

with

a₁:=8e3; a₂:=6e4; a₃:=3e4; a₄:=1.8e8;
b₁:=9.2e17; b₂:=1.1e18; b₃:=4.6e21;
c₁:=8.202046; c₂:=-12.31377; c₃:=-818043.42;

Please, notice, that G (as well as G*F) is a steeply decreasing function on the interval x = 0.025..0.24.

I get "a seemingly correct" result (that means that f increases as x_max intreases), when I try to plot f(x_max) for the following "guessed" options

Digits:=15
integrationmethod:=_d01akc
plot(f,0.21..0.24,color=black)

What is puzzling me is that I get a different "seemingly correct" result, when I modify the integral f by,
at fist, multiplying G by a constant (for example Const:=1e20; G:=Const*exp(c₁+c₂*x+c₃*x⁷) )
and, second, plotting the f divided by this constant:

plot(f/Const,0.21..0.24,color=red)

The following Figure presents the values of f plotted versus x_max with (red curve) and without (black curve) using of the constant Const:

Dear Primes, could you, please, comment on this difference? Because the only indicator that I have (from the analysis of G, F and K) is that f must be a monotonically (and stricktly) increasing function of x_max.

Please, find the maple worksheet in attachment.

Thank you in advance!
Maks

for_primes_numeric_integration_v02.mw