0/Ⱉ𑽇ⵙ✸⛋⦻ⰙⓄ⦻🝊⦻ⓄⰙ⦻⛋✸ⵙ𑽇Ⱉ/𑽇Ⓞ⊞✢✧🝊✧✢⊞Ⓞ𑽇/⦻ꖅ✢✧🝊𐫱𐫰𐫱🝊✧✢ꖅ⦻/YP..⚪ᴥ⚪ᗱᗴ⚪✤⚪Ⓞ⚪ᙁ⚪ߦ⚪◯⚪ᗱᗴ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ИN⚪Ⓞ⚪ꖴ⚪✤⚪ᑐᑕ⚪ᑎ⚪ꗳ⚪◯⚪ᗱᗴ⚪ᴥ⚪ᑎ⚪✤⚪ᗩ⚪ᗯ⚪ᴥ⚪ᑎ⚪ᑐᑕ⚪◯⚪ᗝ⚪ᗱᗴ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᑐᑕ⚪ᗱᗴ⚪ߦ⚪ᔓᔕ⚪𖡼⚪𖡼⚪𖡼⚪𖡼⚪𖡼⚪𖡼⚪ᔓᔕ⚪ߦ⚪ᗱᗴ⚪ᑐᑕ⚪ꖴ⚪ꗳ⚪ꖴ⚪ᗱᗴ⚪ᗝ⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗩ⚪✤⚪ᑎ⚪ᴥ⚪ᗱᗴ⚪◯⚪ꗳ⚪ᑎ⚪ᑐᑕ⚪✤⚪ꖴ⚪Ⓞ⚪ИN⚪◯⚪ᑐᑕ⚪ᑎ⚪ᴥ⚪ᗯ⚪ᗱᗴ⚪◯⚪ߦ⚪ᙁ⚪Ⓞ⚪✤⚪ᗱᗴ⚪ᴥ⚪..PY

<EFBFBD><EFBFBD>import numpy as Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-
import plotly.graph_objects as Y-<1A><><EFBFBD>PU<14><15><15><14>8OT-7<><37><07>%dfY-T-Y-T-Y-df%<1D><15>7<>T-O8<00><14><14><15>PU<1A><><EFBFBD>Y-
from math import *
import mpmath
from ipywidgets import interact,widgets,Text,Layout
from plotly.subplots import make_subplots

Y-<2D>ANO%O<00><>Y-T-Y-T-Y-<2D><>O%ONA<16>Y-=widgets.Text(value='(1-cos(((4)/2)*x))/2',layout=widgets.Layout(width='100%'),description='<00>&<26><15>&A<16>&N<14>&O<16>&%<1D>&<26>$<24>&<26><><EFBFBD>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<26><><EFBFBD>&<26>$<24>&%<1D>&O<16>&N<14>&A<16>&<26><15>&')
Y-%<1D><15><15><15><>AT-<1A><><EFBFBD>%<1D><1A><><EFBFBD>T-<2D><15>dfN<00>%Y-T-Y-T-Y-%<1D>Ndf<15><15>T-<1A><><EFBFBD><EFBFBD>%<1A><><EFBFBD>T-A<16><><EFBFBD><15><15>%Y-=widgets.FloatSlider(min=-4*(4*atan(1)),max=4*(4*atan(1)),value=-2*(4*atan(1)),step=(4*atan(1))/4,layout=widgets.Layout(width='100%'),readout_format='.256f',description='<00>&O<16>&<26>$<24>&%<1D>&<26><><EFBFBD>&<26>%<25>&<26><15><15>&df<15>&N<00>&<26><15>&%<1D>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&%<1D>&<26><15>&N<00>&df<15>&<26><15><15>&<26>%<25>&<26><><EFBFBD>&%<1D>&<26>$<24>&O<16>&')
Y-%<1D><15><15><15><>AT-<2D>N<00><15>T-<2D><15>dfN<00>%Y-T-Y-T-Y-%<1D>Ndf<15><15>T-<2D><15>N<00>T-A<16><><EFBFBD><15><15>%Y-=widgets.FloatSlider(min=-4*(4*atan(1)),max=4*(4*atan(1)),value=2*(4*atan(1)),step=(4*atan(1))/4,layout=widgets.Layout(width='100%'),readout_format='.256f',description='<00>&<26>$<24>&$'<27>&<26>%<25>&<26><15><15>&df<15>&N<00>&<26><15>&%<1D>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&%<1D>&<26><15>&N<00>&df<15>&<26><15><15>&<26>%<25>&$'<27>&<26>$<24>&')
Y-%<1D><15><15><15><>AT-%<1D><15><15>O<00>T-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNT-<2D>O<00><15><15>%T-A<16><><EFBFBD><15><15>%Y-=widgets.IntSlider(min=1,max=16,value=8,layout=widgets.Layout(width='100%'),readout_format='.256f',description='<00>&%<1D>&<26><15><15>&<26><15>&<26>$<24>&<26><07>&<26>%<25>&%<1D>&<26><15><15>&<26>&<26>&O<16>&N<14>&N<00>&<26>%<25>&$'<27>&N<00>&<26><><EFBFBD>&<26>$<24>&<26><07>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<26><07>&<26>$<24>&<26><><EFBFBD>&N<00>&$'<27>&<26>%<25>&N<00>&N<14>&O<16>&<26>&<26>&<26><15><15>&%<1D>&<26>%<25>&<26><07>&<26>$<24>&<26><15>&<26><15><15>&%<1D>&')
Y-%<1D><15><15><15><>AT-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>T-A<16><><EFBFBD><15><15>%Y-=widgets.FloatSlider(min=-2,max=2,value=1,step=1/256,layout=widgets.Layout(width='100%'),readout_format='.256f',description='<00>&<26><00>&<26>%<25>&<26><15><15>&A<16>&<26>&<26>&<26><15>&<26><><EFBFBD>&%<1D>&<26><15>&<26><15>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<26><15>&<26><15>&%<1D>&<26><><EFBFBD>&<26><15>&<26>&<26>&A<16>&<26><15><15>&<26>%<25>&<26><00>&')
Y-%<1D><15><15><15><>AT-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>T-A<16><><EFBFBD><15><15>%Y-=widgets.FloatSlider(min=-2,max=2,value=1,step=1/256,layout=widgets.Layout(width='100%'),readout_format='.256f',description='<00>&<26><><EFBFBD>&<26>%<25>&<26><15><15>&A<16>&<26>&<26>&<26><15>&<26><><EFBFBD>&%<1D>&<26><15>&<26><15>&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<1A>|ܪ&<26><15>&<26><15>&%<1D>&<26><><EFBFBD>&<26><15>&<26>&<26>&A<16>&<26><15><15>&<26>%<25>&<26><><EFBFBD>&')

def Y-<2D>O<16>APUY-T-Y-T-Y-PUA<16>O<16>Y-(x):return max(min(1,x),-1)
def Y-<2D><15><1A><><EFBFBD>N<14>OOPUY-T-Y-T-Y-PUOO<16>N<1A><><EFBFBD><EFBFBD><15>Y-(Y-<2D>ANO%O<00><>Y-T-Y-T-Y-<2D><>O%ONA<16>Y-,x,T-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>T-,T-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>T-):
    Y-<2D>N%<1D>AN8<00>PUO<00>T-NO<00><><1A><><EFBFBD>PUNN<14><>Y-T-Y-T-Y-<2D><>NNPU<1A><>ݴ<EFBFBD>ONT-<2D>OPU<14>8NA<16>%<1D>NY-={Y-<15><15>O<16>NT-NO<00><><1A><><EFBFBD>PUNN<14><>Y-T-Y-T-Y-<2D><>NNPU<1A><>ݴ<EFBFBD>ONT-N<00>O<16><15>Y-:eval(f'lambda*Y-<1A><><EFBFBD>N<00><15>ONdf%<1D>Y-T-Y-T-Y-<2D>%dfNO<16><15>N<1A><><EFBFBD>Y-:mpmath.{Y-<15><15>O<16>NT-NO<00><><1A><><EFBFBD>PUNN<14><>Y-T-Y-T-Y-<2D><>NNPU<1A><>ݴ<EFBFBD>ONT-N<00>O<16><15>Y-}(*Y-<1A><><EFBFBD>N<00><15>ONdf%<1D>Y-T-Y-T-Y-<2D>%dfNO<16><15>N<1A><><EFBFBD>Y-)') for Y-<15><15>O<16>NT-NO<00><><1A><><EFBFBD>PUNN<14><>Y-T-Y-T-Y-<2D><>NNPU<1A><>ݴ<EFBFBD>ONT-N<00>O<16><15>Y- in dir(mpmath)}
    return float(eval(Y-<2D>ANO%O<00><>Y-T-Y-T-Y-<2D><>O%ONA<16>Y-,{'x':x,'Y-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>Y-':T-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>T-,'Y-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>Y-':T-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>T-,'Y-<2D>O<16>APUY-T-Y-T-Y-PUA<16>O<16>Y-':Y-<2D>O<16>APUY-T-Y-T-Y-PUA<16>O<16>Y-,**Y-<2D>N%<1D>AN8<00>PUO<00>T-NO<00><><1A><><EFBFBD>PUNN<14><>Y-T-Y-T-Y-<2D><>NNPU<1A><>ݴ<EFBFBD>ONT-<2D>OPU<14>8NA<16>%<1D>NY-}))
def Y-<1A><><EFBFBD>OA<16>Y-T-Y-T-Y-<2D>AO<1A><><EFBFBD>Y-(Y-<2D>ANO%O<00><>Y-T-Y-T-Y-<2D><>O%ONA<16>Y-='1.4795/Y-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>Y--((x)/(4*atan(1)*Y-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>Y-/2*Y-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>Y-))*1.4795',Y-<1A><><EFBFBD>%<1D><1A><><EFBFBD>T-<2D><15>dfN<00>%Y-T-Y-T-Y-%<1D>Ndf<15><15>T-<1A><><EFBFBD><EFBFBD>%<1A><><EFBFBD>Y-=-2*(4*atan(1)),Y-<2D>N<00><15>T-<2D><15>dfN<00>%Y-T-Y-T-Y-%<1D>Ndf<15><15>T-<2D><15>N<00>Y-=2*(4*atan(1)),Y-%<1D><15><15>O<00>T-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNT-<2D>O<00><15><15>%Y-=8,Y-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>Y-=1,Y-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>Y-=1):
    Y-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNY-=1+2**Y-%<1D><15><15>O<00>T-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNT-<2D>O<00><15><15>%Y-
    
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<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNY-)
    
    Y-<15><15>NA<16><15>T-<2D><15><07>،<>Y-T-Y-T-Y-،<><D88C><15><07>T-<2D><15>AN<14><15>Y-=Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.array([Y-<2D><15><1A><><EFBFBD>N<14>OOPUY-T-Y-T-Y-PUOO<16>N<1A><><EFBFBD><EFBFBD><15>Y-(Y-<2D>ANO%O<00><>Y-T-Y-T-Y-<2D><>O%ONA<16>Y-,Y-<2D><15>NA<16><15>T-<2D><15><07>،<>Y-T-Y-T-Y-،<><D88C><15><07>T-<2D><15>AN<14><15>Y-,Y-<2D>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<2D>Y-,Y-<06><><EFBFBD>T-<2D><15>A8<00><15><>%<1D><15>Y-T-Y-T-Y-<2D><15>%<1D><><EFBFBD>8A<16><15>T-<06><><EFBFBD>Y-) for Y-<2D><15>NA<16><15>T-<2D><15><07>،<>Y-T-Y-T-Y-،<><D88C><15><07>T-<2D><15>AN<14><15>Y- in Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-])
    Y-<15><15>NA<16><15>T-<2D><1A><><EFBFBD><EFBFBD><15>7<><1A><><EFBFBD>Y-T-Y-T-Y-<1A><><EFBFBD>7<EFBFBD><37><15><1A><><EFBFBD><EFBFBD>T-<2D><15>AN<14><15>Y-=Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.cumsum(Y-<15><15>NA<16><15>T-<2D><15><07>،<>Y-T-Y-T-Y-،<><D88C><15><07>T-<2D><15>AN<14><15>Y-)*(Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[1]-Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[0]) if Y-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNY->1 else Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.array([0])
    Y-T-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-d<>Y-T-Y-T-Y-d<>T-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>T-Y-=Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.cumsum(Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.cos(Y-<15><15>NA<16><15>T-<2D><1A><><EFBFBD><EFBFBD><15>7<><1A><><EFBFBD>Y-T-Y-T-Y-<1A><><EFBFBD>7<EFBFBD><37><15><1A><><EFBFBD><EFBFBD>T-<2D><15>AN<14><15>Y-))*(Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[1]-Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[0]) if Y-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNY->1 else Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.array([0])
    Y-T-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-<2D>NY-T-Y-T-Y-<2D>NT-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>T-Y-=Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.cumsum(Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.sin(Y-<15><15>NA<16><15>T-<2D><1A><><EFBFBD><EFBFBD><15>7<><1A><><EFBFBD>Y-T-Y-T-Y-<1A><><EFBFBD>7<EFBFBD><37><15><1A><><EFBFBD><EFBFBD>T-<2D><15>AN<14><15>Y-))*(Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[1]-Y-<15><15>NA<16><15>T-d<>Y-T-Y-T-Y-d<>T-<2D><15>AN<14><15>Y-[0]) if Y-<2D>N<1A><>ݴ<EFBFBD><1A><><EFBFBD>N<00>N
<0A>T-<1A><><EFBFBD>N<00><>O<00>T-Y-T-Y-<2D>O<00><>N<1A><><EFBFBD>T-
<0A>N<14>N<1A><>ݴ<EFBFBD><1A><>ݺNY->1 else Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.array([0])

    if Y-T-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-d<>Y-T-Y-T-Y-d<>T-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>T-Y-[0] !=0 or Y-T-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-<2D>NY-T-Y-T-Y-<2D>NT-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>T-Y-[0] !=0:
        Y-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-d<>Y-T-Y-T-Y-d<>T-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>Y-=Y-<2D>N<EFBFBD>ONNY-0Y-0Y-NNO<16><07>NY-.insert(Y-T-<15><15><1A><><EFBFBD><EFBFBD>N<00><><EFBFBD>%OPUT-d<>Y-T-Y-T-Y-d<>T-PUO%<1D><15><>N<00><1A><><EFBFBD><EFBFBD><15>T-Y-,0,0)
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    else:
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