## Why the integration can not work out when changing...

Dear all,

The program is as follows (The "mw" files are also attached). The integraion "evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))" can not be worked out in several hours, but if the upper limit of x is changed to 0.5 (for example), the integration can be worked out quickly. I have tried to change the program to math model, however, the question still exists. How to solve this problem?

afa:=0.3:
vh:=3.5:
u:=3.12:
mu:=5.5:
gama:=-4*10^(-29)*(1-cos(6*afa))*(1-1*10^(-8)*I):
d1:=1.78*10^(-9):
d2:=48.22*10^(-9):
HBAR:=1.05457266*10^(-34):
ME:=9.1093897*10^(-31):
ELEC:=1.60217733*10^(-19):
Kh:=2.95*10^10:
kc:=sqrt(2*ME*ELEC/HBAR^2):
k:=kc*sqrt(mu):
k0:=sqrt(k^2-k^2*sin(x)^2):
kh:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2 - k^2 * sin(x)^2 * sin(y)^2):
khg:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2):
kg1:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2):
kg2:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2):
k0pl:=sqrt(k^2-k^2*sin(x)^2+kc^2*vh-kc^2*u):
k0mi:=sqrt(k^2-k^2*sin(x)^2-kc^2*vh-kc^2*u):
khpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+kc^2*vh-kc^2*u):
khmi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-kc^2*vh-kc^2*u):
k0plpl:=sqrt(k^2-k^2*sin(x)^2+2*kc^2*vh):
k0mimi:=sqrt(k^2-k^2*sin(x)^2-2*kc^2*vh):
khplpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+2*kc^2*vh):
khmimi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-2*kc^2*vh):
khgplpl:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2+2*kc^2*vh):
khgmimi:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg1plpl:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2+2*kc^2*vh):
kg1mimi:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2-2*kc^2*vh):
kg2plpl:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2+2*kc^2*vh):
kg2mimi:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2-2*kc^2*vh):
A1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
B1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2:
A2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
B2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2:
A3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
B3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2:
A4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
B4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2:
T1:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg1plpl*exp(I*(kg1plpl-conjugate(kg1plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg1mimi*exp(I*(kg1mimi-conjugate(kg1mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg1*exp(I*(kg1-conjugate(kg1))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg1mimi*exp(I*(kg1mimi-conjugate(kg1plpl))*d2)-A1*conjugate(B3)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1mimi))*d2)+conjugate(A1)*(A3-B1)*kg1*exp(I*(kg1-conjugate(kg1plpl))*d2)+A1*conjugate(A3-B1)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1))*d2)+conjugate(B3)*(B1-A3)*kg1*exp(I*(kg1-conjugate(kg1mimi))*d2)+B3*conjugate(B1-A3)*kg1mimi*exp(I*(kg1mimi-conjugate(kg1))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
T2:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg2plpl*exp(I*(kg2plpl-conjugate(kg2plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg2mimi*exp(I*(kg2mimi-conjugate(kg2mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg2*exp(I*(kg2-conjugate(kg2))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg2mimi*exp(I*(kg2mimi-conjugate(kg2plpl))*d2)-A1*conjugate(B3)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2mimi))*d2)+conjugate(A1)*(A3-B1)*kg2*exp(I*(kg2-conjugate(kg2plpl))*d2)+A1*conjugate(A3-B1)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2))*d2)+conjugate(B3)*(B1-A3)*kg2*exp(I*(kg2-conjugate(kg2mimi))*d2)+B3*conjugate(B1-A3)*kg2mimi*exp(I*(kg2mimi-conjugate(kg2))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)):
evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))

 > afa:=0.3: vh:=3.5: u:=3.12: mu:=5.5: gama:=-4*10^(-29)*(1-cos(6*afa))*(1-1*10^(-8)*I): d1:=1.78*10^(-9): d2:=48.22*10^(-9): HBAR:=1.05457266*10^(-34): ME:=9.1093897*10^(-31): ELEC:=1.60217733*10^(-19): Kh:=2.95*10^10: kc:=sqrt(2*ME*ELEC/HBAR^2): k:=kc*sqrt(mu): k0:=sqrt(k^2-k^2*sin(x)^2): kh:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2 - k^2 * sin(x)^2 * sin(y)^2): khg:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2): kg1:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2): kg2:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2): k0pl:=sqrt(k^2-k^2*sin(x)^2+kc^2*vh-kc^2*u): k0mi:=sqrt(k^2-k^2*sin(x)^2-kc^2*vh-kc^2*u): khpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+kc^2*vh-kc^2*u): khmi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-kc^2*vh-kc^2*u): k0plpl:=sqrt(k^2-k^2*sin(x)^2+2*kc^2*vh): k0mimi:=sqrt(k^2-k^2*sin(x)^2-2*kc^2*vh): khplpl:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2+2*kc^2*vh): khmimi:=sqrt(k^2-(Kh-k*sin(x)*cos(y))^2-k^2*sin(x)^2*sin(y)^2-2*kc^2*vh): khgplpl:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2+2*kc^2*vh): khgmimi:=sqrt(k^2-(2*Kh*sin(afa/2)*sin(afa/2)-k*sin(x)*cos(y))^2-(2*Kh*sin(afa/2)*cos(afa/2)+k*sin(x)*sin(y))^2-2*kc^2*vh): kg1plpl:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2+2*kc^2*vh): kg1mimi:=sqrt(k^2-(Kh*cos(Pi/3-afa)-k*sin(x)*cos(y))^2-(Kh*sin(Pi/3-afa)+k*sin(x)*sin(y))^2-2*kc^2*vh): kg2plpl:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2+2*kc^2*vh): kg2mimi:=sqrt(k^2-(Kh*cos(afa)-k*sin(x)*cos(y))^2-(k*sin(x)*sin(y)-Kh*sin(afa))^2-2*kc^2*vh): A1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2: B1:=1/(1+I*ME*gama/(HBAR^2*k0pl))*exp(I*k0pl*d1)/2: A2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2: B2:=1/(1+I*ME*gama/(HBAR^2*khpl))*exp(I*khpl*d1)/2: A3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2: B3:=1/(1+I*ME*gama/(HBAR^2*k0mi))*exp(I*k0mi*d1)/2: A4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2: B4:=1/(1+I*ME*gama/(HBAR^2*khmi))*exp(I*khmi*d1)/2: T1:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg1plpl*exp(I*(kg1plpl-conjugate(kg1plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg1mimi*exp(I*(kg1mimi-conjugate(kg1mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg1*exp(I*(kg1-conjugate(kg1))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg1mimi*exp(I*(kg1mimi-conjugate(kg1plpl))*d2)-A1*conjugate(B3)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1mimi))*d2)+conjugate(A1)*(A3-B1)*kg1*exp(I*(kg1-conjugate(kg1plpl))*d2)+A1*conjugate(A3-B1)*kg1plpl*exp(I*(kg1plpl-conjugate(kg1))*d2)+conjugate(B3)*(B1-A3)*kg1*exp(I*(kg1-conjugate(kg1mimi))*d2)+B3*conjugate(B1-A3)*kg1mimi*exp(I*(kg1mimi-conjugate(kg1))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)): T2:=1/4*Re(abs(A1)^2*k0plpl*exp(I*(k0plpl-conjugate(k0plpl))*d2)+abs(A1)^2*kg2plpl*exp(I*(kg2plpl-conjugate(kg2plpl))*d2)+abs(A2)^2*khplpl*exp(I*(khplpl-conjugate(khplpl))*d2)+abs(A2)^2*khgplpl*exp(I*(khgplpl-conjugate(khgplpl))*d2)+abs(B3)^2*k0mimi*exp(I*(k0mimi-conjugate(k0mimi))*d2)+abs(B3)^2*kg2mimi*exp(I*(kg2mimi-conjugate(kg2mimi))*d2)+abs(B4)^2*khmimi*exp(I*(khmimi-conjugate(khmimi))*d2)+abs(B4)^2*khgmimi*exp(I*(khgmimi-conjugate(khgmimi))*d2)+abs(B1+A3)^2*k0*exp(I*(k0-conjugate(k0))*d2)+abs(B1-A3)^2*kg2*exp(I*(kg2-conjugate(kg2))*d2)+abs(A4-B2)^2*kh*exp(I*(kh-conjugate(kh))*d2)+abs(A4+B2)^2*khg*exp(I*(khg-conjugate(khg))*d2)+conjugate(A1)*B3*k0mimi*exp(I*(k0mimi-conjugate(k0plpl))*d2)+A1*conjugate(B3)*k0plpl*exp(I*(k0plpl-conjugate(k0mimi))*d2)+conjugate(A1)*(B1+A3)*k0*exp(I*(k0-conjugate(k0plpl))*d2)+A1*conjugate(B1+A3)*k0plpl*exp(I*(k0plpl-conjugate(k0))*d2)+conjugate(B3)*(B1+A3)*k0*exp(I*(k0-conjugate(k0mimi))*d2)+B3*conjugate(B1+A3)*k0mimi*exp(I*(k0mimi-conjugate(k0))*d2)-conjugate(A1)*B3*kg2mimi*exp(I*(kg2mimi-conjugate(kg2plpl))*d2)-A1*conjugate(B3)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2mimi))*d2)+conjugate(A1)*(A3-B1)*kg2*exp(I*(kg2-conjugate(kg2plpl))*d2)+A1*conjugate(A3-B1)*kg2plpl*exp(I*(kg2plpl-conjugate(kg2))*d2)+conjugate(B3)*(B1-A3)*kg2*exp(I*(kg2-conjugate(kg2mimi))*d2)+B3*conjugate(B1-A3)*kg2mimi*exp(I*(kg2mimi-conjugate(kg2))*d2)-conjugate(A2)*B4*khmimi*exp(I*(khmimi-conjugate(khplpl))*d2)-A2*conjugate(B4)*khplpl*exp(I*(khplpl-conjugate(khmimi))*d2)+conjugate(A2)*(B2-A4)*kh*exp(I*(kh-conjugate(khplpl))*d2)+A2*conjugate(B2-A4)*khplpl*exp(I*(khplpl-conjugate(kh))*d2)+conjugate(B4)*(A4-B2)*kh*exp(I*(kh-conjugate(khmimi))*d2)+B4*conjugate(A4-B2)*khmimi*exp(I*(khmimi-conjugate(kh))*d2)+conjugate(A2)*B4*khgmimi*exp(I*(khgmimi-conjugate(khgplpl))*d2)+A2*conjugate(B4)*khgplpl*exp(I*(khgplpl-conjugate(khgmimi))*d2)-conjugate(A2)*(A4+B2)*khg*exp(I*(khg-conjugate(khgplpl))*d2)-A2*conjugate(A4+B2)*khgplpl*exp(I*(khgplpl-conjugate(khg))*d2)-conjugate(B4)*(A4+B2)*khg*exp(I*(khg-conjugate(khgmimi))*d2)-B4*conjugate(A4+B2)*khgmimi*exp(I*(khgmimi-conjugate(khg))*d2)): evalf(Int(k*sin(x)*T1,x=0..Pi/2,y=-Pi/6..-Pi/6+afa))
 >

## What is the mathematical definition of "walking fo...

In the website https://en.wikipedia.org/wiki/Geodesic there is an animation of an insect tracing a path on a torus while walking "forward". The caption to the animation says that the path is then by definition a geodesic.

I would like to duplicate this animation in Maple (and other "walking forward" geodesics on other surfaces) which seems to require an exact definition of walking forward but I cannot find such a definition on this or any other website.

Also, I thought that a geodesic is the shortest distance between two points in space, but no such end points are shown in the website's animation. Then how can the word geodesic apply to the insect's path?

## How can a patch on the surface of a sphere display...

The worksheet below displays a sphere with a surface patch defined by the arcs of three intersecting circles on the sphere's surface.

How can the patch be colored differently from the non-patch sphere's surface?

Patch_on_a_Sphere.mw

## Machine learning ...

Is it possible to do machine learning using maplesoft I have 2020 for now

Say I have an excel sheet with one dependent variable and n number of independent variables. I can ask for the number of hidden layers we need.

Then i want to traing the data with 70% of the data for training ,  15% of the data for validation and 15% of the data for testing.

I want some charts may be on the performance of the neural networks.

and get the regression equation formed by this training would be looking to repeat the training until MSE has certain approximation.

## Co-normal products of graphs...

Kind help with Function given two graphs G1 and G2 then co-normal product be the graph G3 given by the function

conormal(G1,G2)

If any other explanation will surely give kind help please will surely acknowlege

## Packing in power...

Given a graph G say and a positive integer k

I am in look out how to remove

edge-disjoint copies of G in G^k

That is edge disjoint copies of G into its power graph all possible ways

Again it is the maximum number of copies I means

Keeping this particular way can someone help kind help please

I will surely acknowledge it

G into to GraphPower(G,k)

## Can these ODEs be solved?...

Why does an attempt to solve the ODEs in the uploaded worksheet fail and how can this error be removed so they can be solved?

Unable_to_convert.mw

## Extract subgraphs from a supergraph...

Problem 1)   Give graph G1 and a graph G2  the problem is to extract maximum isomorphic copies of G1 from G2 such that it has no edge intersection maximum number is floor((number of edges of G2)/(number of edges of G1)) and display the Edge sets of those isomorphic graphs and the graph formed by the remaining edges sometimes their may be no remaing edges too.  Need all possible such copies.

Problem 2) Give graph G1 and a graph G2  the problem is to extract maximum isomorphic copies of G1 from G2 such that each copy has  exactly one edge intersection with each of the copies and that one edge intersection occurs only between those two copies and  display the Edge sets of those isomorphic graphs . Need all possible such copies.

I had written this c++ code years back for problem 2 which i have forgotten kind help if possible to make it better with maplesoft.

Please take your time. Kind help help plese it will be very helpful it is of real help.

orthogonal.txt

I had written this c++ code years back for problem 1 which i have forgotten kind help if possible to make it better with maplesoft.

Please take your time. Kind help help plese it will be very helpful it is of real help.

decom.txt

Need to maintain memory space as graph size is a little big may be

would usage of database or any other be useful dont know I had done those code in c++ long back which i forgotten logic too.

I would surely acknowledge for this great work as much as I can much more than I can acknowlege too

I am using Maple 2020

## How to solve this integral?...

I am trying to solce eq (2) by integration. But maple integrate only 1st term in eq. Why not other two terms?

Solve_integral.mw

## Where can I get advice re a faster Maple processin...

The computer on which I have been executing Maple worksheets for the past six years (CPU: i7 - 5820K, 6 core, 3.3 GHz, 5th generation) is now significantly slower than new machines.

I don't know how to interpret public specifications of potential replacement machines into their actual future performance with Maple.

Please give me or direct me to any advice which would enable me to knowledgeably purchase a much faster processor of Maple code.

## Why maple give empty solutions?...

Why maple give empty solutions? See ref. (12) in the attached wokrsheet. Is there anything missing when deriving Sols?

sols_tw.mw

## Questions re using Maple cloud...

I want to create and modify the same worksheet at different times on two different computers in two different locations.

To avoid transferring files between the two machines, it seems most convenient to reference all objects within Maple cloud.

I am a beginner at this and have several questions:

1) I have downloaded the DirectSearch package as directed in help text but the only result from issuing the command kernelopts(toolboxdir) is " ".

How can I establish a path which enables my worksheet to execute commands within this package?

2) How can my worksheet invoke procedures within my .mla file referencing only objects in Maple cloud?

How can I update (save and delete procedures) within my .mla file?

## How to integrate...

Hello my friends
Please help me solve the integration problem in the attached Maple code below (why was the integration not done in u[4]?) ... Thank you very much

 > u[1] :=  1/3*t^3*x + 2*t*x + (-1)*0.7522527780*t^(3/2)*x + (-1)*0.1719434922*t^(7/2)*x + (-1)*0.01587301587*t^7*x + (-1)*0.1333333333*t^5*x
 (1)
 > u[2] := subs(t=Tau,u[1]);
 (2)
 > u[3]:= int(u[2],Tau = 0 .. t);
 (3)
 > u[4]:= int((t-Tau)^(-0.5)*u[2],Tau = 0 .. t);
 (4)

## Help writing code...

Hello my friends
How can I write the results inside the Maple code as in the picture? That is, writing the results in terms of gamma and alpha

## Common legend for different figures...

Hello,

Is it possible to have a common legend for different figures? I can plot them as Array of Plots (below) but then they each have a legend.

Is it possible to have the two figures side by side and a common legend in the middle?

Thank you!

restart:
with(plots):
A := Array(1 .. 2):
A[1] := plot([2*sin(x), 3*sin(x)], x = -Pi .. Pi, labels = [x, b*sin(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
A[2] := plot([2*cos(x), 3*cos(x)], x = -Pi .. Pi, labels = [x, b*cos(x)], color = [blue, red], legend = ["Case of b=2", "Case of b=3"]):
display(A);

 1 2 3 4 5 6 7 Last Page 2 of 52
﻿