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In this article, we consider an anisotropic viscous cosmological model having LRS Bianchi type I spacetime with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity. We investigate the modified <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>Q</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity with form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>Q</mi><mo>)</mo></mrow><mo>=</mo><mi>α</mi><msup><mi>Q</mi><mn>2</mn></msup><mo>+</mo><mi>β</mi></mrow></semantics></math></inline-formula>, where <i>Q</i> is the non-metricity scalar and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> are the positive constants. From the modified Einstein’s field equation having the viscosity coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ξ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>ξ</mi><mn>0</mn></msub><mi>H</mi></mrow></semantics></math></inline-formula>, the scale factor is derived as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>2</mn><mspace width="3.33333pt"></mspace><mi>s</mi><mi>i</mi><mi>n</mi><mi>h</mi><mfenced separators="" open="(" close=")"><mfrac><mrow><mi>m</mi><mo>+</mo><mn>2</mn></mrow><mn>6</mn></mfrac><msqrt><mfrac><msub><mi>ξ</mi><mn>0</mn></msub><mrow><mi>α</mi><mo>(</mo><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></mfrac></msqrt><mi>t</mi></mfenced></mrow></semantics></math></inline-formula>. We apply the observational constraints on the apparent magnitude <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>χ</mi><mn>2</mn></msup></semantics></math></inline-formula> test formula with the observational data set such as JLA, Union 2.1 compilation and obtained the best approximate values of the model parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>,</mo><mi>α</mi><mo>,</mo><msub><mi>H</mi><mn>0</mn></msub><mo>,</mo><msub><mi>ξ</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>. We find a transit universe which is accelerating at late times. We also examined the bulk viscosity equation of state (EoS) parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mi>v</mi></msub></semantics></math></inline-formula> and derived its current value satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>v</mi></msub><mo><</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></mrow></semantics></math></inline-formula>, which shows the dark energy dominating universe evolution having a cosmological constant, phantom, and super-phantom evolution stages. It tends to the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula> cold dark matter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM) value (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ω</mi><mi>v</mi></msub><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>) at late times. We also estimate the current age of the universe as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>t</mi><mn>0</mn></msub><mo>≈</mo><mn>13.6</mn></mrow></semantics></math></inline-formula> Gyrs and analyze the statefinder parameters with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>r</mi><mo>)</mo><mo>→</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula> as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>→</mo><mo>∞</mo></mrow></semantics></math></inline-formula>.