restart;
  with(plots):
  pu:=1/(2)*exp(-u^(2));
  ode:= diff(x(u), u, u) +1/(2)*pu*x(u) = 0:
  cons1:= x(0)=1, D(x)(0)=0:
  cons2:= x(2)=0, D(x)(2)=0:
  sol1:= dsolve([ode, cons1], numeric);
  sol2:= dsolve([ode, cons2], numeric);
  display( [ plot( pu,
                   u=-2..2,
                   color=black
                 ),
             odeplot( sol1,
                     [u,x(u)],
                     u=-2..2,
                     color=blue
                  ),
             odeplot( sol2,
                      [u,x(u)],
                      u=-2..2,
                      color=red
                    )
            ]
          );

  restart;
  p(u):= 1/2*exp(-u^2):
  odeSys:= diff(x(u), u, u) + 1/2*p(u)*x(u) = 0,
           diff(y(u), u, u) - 1/2*p(u)*y(u) = 0,
           diff(v(u), u, u) + 1/4*diff(p(u), u)*(x(u)^2 - y(u)^2) + p(u)*(x(u)*diff(x(u), u) - y(u)*diff(y(u), u)) = 0:
  conds:= v(0) = 1,
          D(v)(0) = 0,
          y(0) = 1,
          D(y)(0) = 0,
          x(0) = 1,
          D(x)(0) = 0:
  sol:= dsolve( [ odeSys, conds] ,
                numeric
              );
  plots:-odeplot( sol,
                  [ [u, p(u)],
                    [u, x(u)],
                    [u, y(u)],
                    [u, v(u)]
                  ],
                  u = -8 .. 8,
                  color = [red, blue, green, black],
                  legend = ['p(u)', x(u), y(u), v(u)]
                );

  with(plots):
  interface(version);

  display
  ( tubeplot
    ( [cos(t), 0, sin(t)],
      t = -Pi .. Pi, radius = .2
    ),
    tubeplot
    ( [cos(t), sin(t), 0],
      t = -Pi .. Pi, radius = .2
    ),
    style = surface,
    color = [red, red]
  );
  display
  ( tubeplot
    ( [cos(t), 0, sin(t)],
      t = -Pi .. Pi, radius = .2,
      color = [red]
    ),
    tubeplot
    ( [cos(t), sin(t), 0],
      t = -Pi .. Pi, radius = .2,
      color = [red]
    ),
    style = surface
  );

restart;

kernelopts(version);

with(plots):

display(
        tubeplot([cos(t), 0, sin(t)], t=-Pi..Pi, radius=0.2),
        tubeplot([cos(t), sin(t), 0], t=-Pi..Pi, radius=0.2),
style=surface, color=[red,green]);
plottools:-getdata(%, 'includecolor')[1..2,4];

display(
        tubeplot([cos(t), 0, sin(t)], t=-Pi..Pi, radius=0.2),
        tubeplot([cos(t), sin(t), 0], t=-Pi..Pi, radius=0.2),
style=surface, color=[red,red]);
plottools:-getdata(%, 'includecolor')[1..2,4];

display(
        tubeplot([cos(t), 0, sin(t)], t=-Pi..Pi, radius=0.2, color=red),
        tubeplot([cos(t), sin(t), 0], t=-Pi..Pi, radius=0.2, color=red),
style=surface);
plottools:-getdata(%, 'includecolor')[1..2,4];

  restart:
  interface(version);
  plot(140^t*exp(-140)/t!, t = 0 .. 300);
  Digits:=16:
  plot(140^t*exp(-140)/t!, t = 0 .. 300);
  Digits:=10:

restart:
with(plots):
with(plottools):
with(Student[LinearAlgebra]):
#infolevel[Student[LinearAlgebra]]:=1: # why does this exist? Comment out
#with(LinearAlgebra): # why does this exist? Comment out
#with(linalg,vector,matrix,crossprod,angle): # why does this exist? Comment out
pu:=Pi/180:
evalf(pu):
d:=172;t := (2 *Pi*((d - 1) / 365)):Phi:=37.52*pu;

d:=72: t:=(2*Pi*((d-1)/365)):
Phi:=37.52*pu:

delta:=evalf(((0.322003-22.971*cos(t)-0.357898*cos(2*t)-0.14398*cos(3*t)+3.94638*sin(t)+0.019334*sin(2*t)+0.05928*sin(3*t)))*pu);:

ws:=evalf(-arccos(-tan(Phi)*tan(delta)));
# why does this next command exist? - comment out
#
# evalf(ws);

alpha:=arcsin(cos(Phi)*cos(delta)*cos(omega)+sin(Phi)*sin(delta)):
#
# the following is only used as a constituent of
# the variable 'Colm' which is not used anywhere
# in this worksheet, so why does this exist?
#
# Comment it out
#
# colm1:=evalf(seq(alpha,omega=ws..0,0.01)/pu):

gama:=arccos((sin(delta)-sin(alpha)*sin(Phi))/(cos(alpha)*cos(Phi))):
#
# the following is only used as a constituent of
# the variable 'Colm' which is not used anywhere
# in this worksheet, so why does this exist?
#
# Comment it out
#
# colm2:=evalf(seq(gama,omega=ws..0,0.01)/pu):

x:=cos(alpha)*cos(gama);
#
# the following is only used as a constituent of
# the variable 'Colm' which is not used anywhere
# in this worksheet, so why does this exist?
#
# Comment it out
#
# colm3:=(seq(x,omega=ws..0,0.01)):

y:=cos(alpha)*sin(gama);
#
# the following is only used as a constituent of
# the variable 'Colm' which is not used anywhere
# in this worksheet, so why does this exist?
#
# Comment it out
#
# colm4:=(seq(y,omega=ws..0,0.01)):

z:=sin(alpha);
#
# the following is only used as a constituent of
# the variable 'Colm' which is not used anywhere
# in this worksheet, so why does this exist?
#
# Comment it out
#
# colm5:=(seq(z,omega=ws..0,0.01)):
#
# The variable Colm is not used anywhere in this worksheet
# so why does the following exist? Comment it out
#
# Colm:=(<colm1>,<colm2>,<colm3>,<colm4>,<colm5>):

c:=sphere([0,0,0],1,color=white,transparency=0.5):             
h3:=spacecurve([-x,-y,z],omega=ws..0,color=green,thickness=5):
h4:=spacecurve([-x,y,z],omega=ws..0,color=blue,thickness=5):
blu:=op([1,1], h4):
whattype(blu);
gre:=op([1,1], h3):
whattype(gre);
#
# Observation - both 'blu' and 'gre' are Arrays whos entries
# may be accessed using square brackets - as in blu[1,1] etc
#
# Loop index for the following started from 0 when the indexing
# for blu starts from 1, so fixed this
#
# But why do you write stuff out to a file and then read the
# the same stuff back again - this is completely pointless.
#
# A total waste of time and space on your hard drive
#
for i from 1 to 200 do
     MyFile := cat(currentdir(), "/PP.txt"):
     writeto(MyFile):
#
# 'blu' is an array whise lements can be accessed using square brackets
# as in blu[1,1]. As used below with round brackets  'blu' is a function/
# procedure with supplied arguments - no relation to the Array previously
# defined - so I have no idea what the rest of this loop is attempting to
# achieve. I can pretty much guarantee that whatever the OP wnats, this isn't
# going to do it
#
#
     PlanePlot(blu(i,1)*xx+blu(i,2)*yy+blu(i,3)*zz=0,[xx,yy,zz], showbasis ):
     close(MyFile):


     writeto(terminal):
     with(StringTools):

     fine:= readline(MyFile):
     while fine <> 0 do
           last := fine:
           fine := readline(MyFile):
           if   fine <> 0 and Search("basis vectors:", fine) =1
           then bv := StringSplit(fine, "basis vectors:")[2]:
                bv1||i, bv2||i := parse(%):
           end if:
     end do:
od:
##`basis vector 1` = bv1;
##`basis vector 2` = bv2;# benim işime yarayan vektör

#
# Following commmand will 'Error' because 'h5' is
# not defined anywhere - exactly how do you think
# you can plot something whihc is undefined????
#
# Comment it out
#
#  display(c,h4,h3,h5);
#
# 'c' 'h3' and 'h4' have been defined so can be
# displayed
#
  display(c,h4,h3);

#
# Hmmmmmm we seem to be repeating ourselves. Writing stuuf out to a
# hard drive, then reading the same stuff back in again.
#
# why? WHY? WHY?
#
#
MyFile := cat(currentdir(), "/PP.txt"):
writeto(MyFile):
#
# Well this won't work because it requires 'blu' to be a function/
# procedure which accepts two arguments. OP probably wants entries
# of the Array 'blu' whihc would require square brackets - as in
# blu[1,1].
#
# But we still won't get anywhere because the name 'as' is not
# defined anywhere in this worksheet
#
PlanePlot(blu(as,1)*xx+blu(as,2)*yy+blu(as,3)*zz=0,[xx,yy,zz], showbasis ):
close(MyFile):


writeto(terminal):
with(StringTools):

fine:= readline(MyFile):
while fine <> 0 do
   last := fine:
   fine := readline(MyFile):
   if   fine <> 0 and Search("basis vectors:", fine) =1
   then bv := StringSplit(fine, "basis vectors:")[2]:
        bv1, bv2 := parse(%):
   end if:
end do:

#`basis vector 1` = bv1;
#`basis vector 2` = bv2;# benim işime yarayan vektör

Error, unsupported type of index, as

  restart;
  interface(version);
  with(plots):

  eq1:= diff(f(x), x$3)
        +
        1/2*(1-phi)^2.5*(1-phi+phi*rho__s/rho__f1)*(eta*cos__omega + f(x)*sin__omega)*diff(f(x), x$2)
        +
        (1-phi)^2.5*M*sin(alpha)^2*(1-diff(f(x),x))
        +
        (1-phi)^2.5*(1-phi+phi*rho__beta__s/rho__beta__f1)*lambda__T*theta(x);

  eq2:= K__nf/K__f*diff(theta(x),x$2)
        +
        Pr/2*(eta*cos__omega + f(x)*sin__omega)*diff(theta(x),x);
#
# The OP's original list of boundary conditions contained f(1)=0.
# In a 1-dimensional BVP only two boundaries are allowed, so the
# condition f(1)=0 has been "replaced" by the condition
#
#    D(f)(0) = val
#
# A "shooting" method will be used later to determine a value for
# "val", whihc ensures that the original BC ( ie f(1)=0 ) is
# satisfied
#
  bcs := f(0) = 0, D(f)(0) = val, f(10) = 1, theta(0) = 1, theta(10) = 0;

  params:= [ K__f=0.613, K__nf=0.6842, M=1, Pr=6.2,
             alpha=0, eta=0, phi=0.05, rho__f1=997.1,
             rho__s=5200, cos__omega=1, lambda__T=0,
             rho__beta__f1=20939.1, rho__beta__s=997.1,
             sin__omega=1
           ];
#
# So the ODE system with all parameter values inserted is
#
  odesys:=eval([eq1, eq2], params);

#
# The shooting method
#
# This determines a value for D(f)(0) such that the
# OP's original desired condition f(1)=0 is satisfied
#
  SM:= proc( shoot )
             local ans:
             if type( shoot, numeric)
             then ans:= dsolve
                        ( eval
                          ( [odesys[], bcs],
                            val=shoot
                          ),
                          numeric
                        ):
                  return rhs(ans(1)[2]);
             else return 'procname(_passed)'
             fi;
       end proc:
  sv:= fsolve( SM );

#
# Solve the system
#
  sol:= dsolve
        (  eval
           ( [odesys[], bcs],
             val=sv
           ),
          numeric
        ):
#
# Check that when x=1, f(x)=0, which was OP's desired condition
#
  sol(1)[1..2];
#
# Plot the results
#
  odeplot
  ( sol,
    [ [x, f(x)],
      [x, theta(x)]
    ],
    x = 0 .. 10,
    color=[red, blue],
    legend=[typeset(f(x)), typeset(theta(x))]
  );